iProver---3.9.4.THM-CRf.s

%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM926+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n018.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 : Fri Sep 25 02:27:21 PM UTC 2026

% Result   : Theorem 123.21s 22.59s
% Output   : CNFRefutation 124.27s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f5156ERROR: Could not build tree for root c_126603ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    is_int(one_one_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

fof(f3,axiom,
    is_int(undefined_int(int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Int__Oint) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => is_int(multInv(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int2_OMultInv) ).

fof(f5,axiom,
    ! [X0] :
      ( is_int(X0)
     => is_int(zfact(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_IntFact_Ozfact) ).

fof(f8,axiom,
    is_int(min),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OMin) ).

fof(f9,axiom,
    is_int(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OPls) ).

fof(f10,axiom,
    ! [X0] :
      ( is_int(X0)
     => is_int(number_number_of_int(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => is_int(legendre(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Residues_OLegendre) ).

fof(f13,axiom,
    ! [X0] : is_int(twoSqu1241645765sum2sq(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_TwoSquares__Mirabelle__enbualjaop_Osum2sq) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => is_int(inv(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WilsonRuss_Oinv) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => is_int(hAPP_int_int(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).

fof(f19,axiom,
    ! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).

fof(f22,axiom,
    is_int(m),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m) ).

fof(f23,axiom,
    is_int(s1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s1____) ).

fof(f24,axiom,
    is_int(s),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s____) ).

fof(f25,axiom,
    is_int(t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_t____) ).

fof(f26,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).

fof(f27,axiom,
    ( t = one_one_int
   => ? [X0,X1] :
        ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
        & is_int(X1)
        & is_int(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(f28,axiom,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
   => ? [X0,X1] :
        ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
        & is_int(X1)
        & is_int(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(f29,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).

fof(f30,axiom,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).

fof(f31,axiom,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).

fof(f32,axiom,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).

fof(f34,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit1(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).

fof(f35,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).

fof(f36,axiom,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).

fof(f37,axiom,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__sum) ).

fof(f41,axiom,
    ! [X0] : hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cube__square) ).

fof(f45,axiom,
    ! [X0] : hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(f46,axiom,
    ! [X0] : hAPP_real_real(times_times_real(X0),X0) = hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(f47,axiom,
    ! [X0] : hAPP_nat_nat(times_times_nat(X0),X0) = hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(f51,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(f52,axiom,
    ! [X0,X1] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(f53,axiom,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(f54,axiom,
    ! [X0] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__special_I2_J) ).

fof(f55,axiom,
    ! [X0] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).

fof(f56,axiom,
    ! [X0] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).

fof(f57,axiom,
    ! [X0] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).

fof(f60,axiom,
    ~ ! [X0] :
        ( is_int(X0)
       => hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) != hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).

fof(f61,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zle__refl) ).

fof(f62,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zle__linear) ).

fof(f65,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zle__trans) ).

fof(f66,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
         => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zle__antisym) ).

fof(f67,axiom,
    ! [X0,X1,X2] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(f68,axiom,
    ! [X0,X1,X2] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(f69,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(f75,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
    <=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).

fof(f76,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
    <=> ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).

fof(f78,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__number__of) ).

fof(f80,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_le__number__of) ).

fof(f81,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).

fof(f82,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(f83,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(f84,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(f87,axiom,
    ! [X0] : hAPP_nat_nat(times_times_nat(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).

fof(f88,axiom,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).

fof(f90,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit1(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).

fof(f92,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit1(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).

fof(f95,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit0(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit0(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__number__of__int__code) ).

fof(f100,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code) ).

fof(f101,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X0)),hAPP_int_int(plus_plus_int(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).

fof(f102,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).

fof(f103,axiom,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
       => ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
           => hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
           => hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(X1) ) ) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
       => hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).

fof(f104,axiom,
    number_number_of_nat(bit1(pls)) = one_one_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).

fof(f106,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).

fof(f107,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).

fof(f109,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit0(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).

fof(f111,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit1(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J) ).

fof(f113,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).

fof(f114,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).

fof(f115,axiom,
    hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zprime__2) ).

fof(f116,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
     => ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
       => hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).

fof(f129,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(f130,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(f131,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(f135,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(f136,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(f137,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(f138,axiom,
    ! [X0,X1] : hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(f139,axiom,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(f140,axiom,
    ! [X0,X1] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(f144,axiom,
    ! [X0,X1] :
      ( hBOOL(member_int(X0,X1))
    <=> hBOOL(hAPP_int_bool(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mem__def) ).

fof(f145,axiom,
    ! [X0] : collect_int(X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Collect__def) ).

fof(f149,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(f150,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(f151,axiom,
    ! [X0,X1,X2] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(f154,axiom,
    ! [X0,X1,X2] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(f155,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(f157,axiom,
    ! [X0,X1,X2] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(f158,axiom,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f159,axiom,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f160,axiom,
    ! [X0,X1] : hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f161,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( number_number_of_int(X0) = number_number_of_int(X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_eq__number__of) ).

fof(f162,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( number267125858f_real(X0) = number267125858f_real(X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_eq__number__of) ).

fof(f166,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( bit1(X0) = bit1(X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_rel__simps_I51_J) ).

fof(f167,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( bit0(X0) = bit0(X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_rel__simps_I48_J) ).

fof(f168,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_zmult__assoc) ).

fof(f169,axiom,
    ! [X0,X1] : hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_zmult__commute) ).

fof(f170,axiom,
    ! [X0] :
      ( is_int(X0)
     => number_number_of_int(X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_number__of__is__id) ).

fof(f171,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_zadd__assoc) ).

fof(f172,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_zadd__left__commute) ).

fof(f173,axiom,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zadd__commute) ).

fof(f176,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit0(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rel__simps_I16_J) ).

fof(f178,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_rel__simps_I4_J) ).

fof(f179,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_rel__simps_I22_J) ).

fof(f181,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit1(X1)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rel__simps_I32_J) ).

fof(f182,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rel__simps_I27_J) ).

fof(f183,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_rel__simps_I21_J) ).

fof(f185,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__even__eq) ).

fof(f186,axiom,
    ! [X0,X1] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__even__eq) ).

fof(f187,axiom,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power__even__eq) ).

fof(f188,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__special_I4_J) ).

fof(f189,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__special_I4_J) ).

fof(f190,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__special_I2_J) ).

fof(f191,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__special_I2_J) ).

fof(f192,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__special_I4_J) ).

fof(f193,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__special_I4_J) ).

fof(f194,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__special_I2_J) ).

fof(f195,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_le__special_I2_J) ).

fof(f205,axiom,
    ! [X0,X1,X2,X3] :
      ( ( is_int(X3)
        & is_int(X2)
        & is_int(X1)
        & is_int(X0) )
     => ( ( X0 != X1
          & X2 != X3 )
      <=> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_crossproduct__noteq) ).

fof(f206,axiom,
    ! [X0,X1,X2,X3] :
      ( ( X0 != X1
        & X2 != X3 )
    <=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_crossproduct__noteq) ).

fof(f207,axiom,
    ! [X0,X1,X2,X3] :
      ( ( X0 != X1
        & X2 != X3 )
    <=> hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_crossproduct__noteq) ).

fof(f208,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(f210,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(f213,axiom,
    ! [X0] : hAPP_real_real(times_times_real(X0),one_one_real) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(f220,axiom,
    ! [X0] : bit1(X0) != pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rel__simps_I46_J) ).

fof(f222,axiom,
    ! [X0,X1] : bit1(X0) != bit0(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rel__simps_I50_J) ).

fof(f226,axiom,
    bit0(pls) = pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Bit0__Pls) ).

fof(f232,axiom,
    ! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Bit0__def) ).

fof(f233,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_int_int(times_times_int(X0),one_one_int) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zmult__1__right) ).

fof(f234,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_int_int(times_times_int(one_one_int),X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zmult__1) ).

fof(f235,axiom,
    ! [X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_times__numeral__code_I5_J) ).

fof(f237,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_zadd__zmult__distrib2) ).

fof(f238,axiom,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_plus__numeral__code_I9_J) ).

fof(f240,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
       => hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_semiring__mult__number__of) ).

fof(f243,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
       => hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_semiring__add__number__of) ).

fof(f245,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_power2__ge__self) ).

fof(f255,axiom,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(f256,axiom,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X0)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(f257,axiom,
    ! [X0,X1] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(f258,axiom,
    ! [X0] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(f259,axiom,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),X0) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(f260,axiom,
    ! [X0] : hAPP_real_real(plus_plus_real(X0),X0) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(f265,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),X2)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_mult__number__of__left) ).

fof(f266,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(number267125858f_real(X1)),X2)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mult__number__of__left) ).

fof(f269,axiom,
    ! [X0,X1] : number_number_of_int(hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_number__of__mult) ).

fof(f270,axiom,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(times_times_int(X0),X1)) = hAPP_real_real(times_times_real(number267125858f_real(X0)),number267125858f_real(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_number__of__mult) ).

fof(f271,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__number__of__left) ).

fof(f272,axiom,
    ! [X0,X1,X2] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(plus_plus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__number__of__left) ).

fof(f274,axiom,
    ! [X0,X1] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__number__of__eq) ).

fof(f275,axiom,
    ! [X0,X1] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_number__of__add) ).

fof(f276,axiom,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_number__of__add) ).

fof(f278,axiom,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(bit0(X0)),bit1(X1)) = bit1(hAPP_int_int(plus_plus_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_add__Bit0__Bit1) ).

fof(f279,axiom,
    ! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Bit1__def) ).

fof(f280,axiom,
    ! [X0] : number_number_of_int(bit1(X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_number__of__Bit1) ).

fof(f281,axiom,
    ! [X0] : number267125858f_real(bit1(X0)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0))),number267125858f_real(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_number__of__Bit1) ).

fof(f286,axiom,
    number_number_of_int(bit1(pls)) = one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).

fof(f288,axiom,
    number267125858f_real(bit1(pls)) = one_one_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_semiring__numeral__1__eq__1) ).

fof(f294,axiom,
    ! [X0,X1] : hAPP_int_int(times_times_int(bit1(X0)),X1) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(X0),X1))),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_mult__Bit1) ).

fof(f295,axiom,
    ! [X0] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(bit0(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_double__number__of__Bit0) ).

fof(f296,axiom,
    ! [X0] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) = number267125858f_real(bit0(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).

fof(f297,axiom,
    ! [X0] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).

fof(f298,axiom,
    ! [X0] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_power3__eq__cube) ).

fof(f299,axiom,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_power3__eq__cube) ).

fof(f300,axiom,
    ! [X0] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_quartic__square__square) ).

fof(f306,axiom,
    ! [X0] : hAPP_int_int(times_times_int(X0),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).

fof(f308,axiom,
    ! [X0] : hAPP_real_real(times_times_real(X0),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_semiring__mult__2__right) ).

fof(f314,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_p0) ).

fof(f315,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).

fof(f316,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(zprime,X0))
       => ( X0 != number_number_of_int(bit0(bit1(pls)))
         => ( X0 != number_number_of_int(bit1(bit1(pls)))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X0)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_prime__g__5) ).

fof(f317,axiom,
    twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).

fof(f319,axiom,
    ! [X0] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),number_number_of_nat(bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_four__x__squared) ).

fof(f320,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).

fof(f321,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_power__less__power__Suc) ).

fof(f322,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_power__less__power__Suc) ).

fof(f323,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).

fof(f324,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_power__gt1__lemma) ).

fof(f325,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_power__gt1__lemma) ).

fof(f329,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).

fof(f330,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_power__increasing__iff) ).

fof(f331,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_power__increasing__iff) ).

fof(f332,axiom,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(s1),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).

fof(f333,axiom,
    ( hBOOL(hAPP_int_bool(zcong(s1,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_s0p) ).

fof(f334,axiom,
    ? [X0] :
      ( ! [X1] :
          ( is_int(X1)
         => ( ( hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
           => X1 = X0 ) )
      & hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      & is_int(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).

fof(f335,axiom,
    ~ ! [X0] :
        ( is_int(X0)
       => ~ ( hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) ).

fof(f336,axiom,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s1),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_s1) ).

fof(f340,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).

fof(f341,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_le__imp__power__dvd) ).

fof(f342,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_le__imp__power__dvd) ).

fof(f343,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).

fof(f344,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_dvd__power__le) ).

fof(f345,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_dvd__power__le) ).

fof(f346,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X2)),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).

fof(f347,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X2)),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__le__dvd) ).

fof(f348,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X2)),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_power__le__dvd) ).

fof(f349,axiom,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X0) )
     => ( hAPP_nat_int(power_power_int(X0),X1) = hAPP_nat_int(power_power_int(X2),X1)
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
           => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
             => X0 = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).

fof(f350,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) = hAPP_nat_nat(power_power_nat(X2),X1)
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
           => X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_power__eq__imp__eq__base) ).

fof(f351,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_real(power_power_real(X0),X1) = hAPP_nat_real(power_power_real(X2),X1)
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
           => X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_power__eq__imp__eq__base) ).

fof(f352,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
       => ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_zdvd__not__zless) ).

fof(f353,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
             => X1 = X0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_zdvd__antisym__nonneg) ).

fof(f355,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).

fof(f356,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_dvd__power__same) ).

fof(f358,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => ( X1 != zero_zero_int
       => hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_field__power__not__zero) ).

fof(f359,axiom,
    ! [X0,X1] :
      ( X1 != zero_zero_real
     => hAPP_nat_real(power_power_real(X1),X0) != zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_field__power__not__zero) ).

fof(f360,axiom,
    ! [X0] :
      ( ( X0 != zero_zero_nat
       => hAPP_nat_int(power_power_int(zero_zero_int),X0) = zero_zero_int )
      & ( X0 = zero_zero_nat
       => hAPP_nat_int(power_power_int(zero_zero_int),X0) = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_power__0__left) ).

fof(f362,axiom,
    ! [X0] :
      ( ( X0 != zero_zero_nat
       => hAPP_nat_real(power_power_real(zero_zero_real),X0) = zero_zero_real )
      & ( X0 = zero_zero_nat
       => hAPP_nat_real(power_power_real(zero_zero_real),X0) = one_one_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power__0__left) ).

fof(f364,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).

fof(f365,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_power__strict__mono) ).

fof(f366,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
         => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_power__strict__mono) ).

fof(f375,axiom,
    ! [X0] : hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(f379,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( X0 = hAPP_int_int(plus_plus_int(X0),X1)
      <=> X1 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_add__0__iff) ).

fof(f381,axiom,
    ! [X0,X1] :
      ( X0 = hAPP_real_real(plus_plus_real(X0),X1)
    <=> X1 = zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add__0__iff) ).

fof(f382,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hAPP_int_int(plus_plus_int(X0),X0) = zero_zero_int
      <=> X0 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_double__eq__0__iff) ).

fof(f383,axiom,
    ! [X0] :
      ( hAPP_real_real(plus_plus_real(X0),X0) = zero_zero_real
    <=> X0 = zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_double__eq__0__iff) ).

fof(f384,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_Pls__def) ).

fof(f386,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_zadd__0) ).

fof(f387,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_int_int(plus_plus_int(X0),zero_zero_int) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_zadd__0__right) ).

fof(f390,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_zero__le__power) ).

fof(f391,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_power__mono) ).

fof(f392,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_power__mono) ).

fof(f393,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_power__mono) ).

fof(f394,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_zero__less__power) ).

fof(f396,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_zero__less__power) ).

fof(f397,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X2),one_one_int),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),X0)),one_one_int),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_zcong__zpower__zmult) ).

fof(f398,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2))))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_zdvd__reduce) ).

fof(f399,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X4))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_zdvd__period) ).

fof(f400,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).

fof(f401,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_power__less__imp__less__base) ).

fof(f402,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1)))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_power__less__imp__less__base) ).

fof(f403,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),one_one_int))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_power__decreasing) ).

fof(f404,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),one_one_nat))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_power__decreasing) ).

fof(f405,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),one_one_real))
         => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_power__decreasing) ).

fof(f406,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).

fof(f407,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_power__strict__decreasing) ).

fof(f408,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),one_one_real))
         => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_power__strict__decreasing) ).

fof(f410,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real))
    <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_even__less__0__iff) ).

fof(f411,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_sum__squares__eq__zero__iff) ).

fof(f413,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ( is_int(X4)
        & is_int(X1)
        & is_int(X0) )
     => ( X4 != zero_zero_int
       => ( ( X0 != X1
            & X2 = X3 )
         => hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(X4),X0)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).

fof(f414,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( X4 != zero_zero_nat
     => ( ( X0 != X1
          & X2 = X3 )
       => hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X4),X0)) != hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_add__scale__eq__noteq) ).

fof(f415,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( X4 != zero_zero_real
     => ( ( X0 != X1
          & X2 = X3 )
       => hAPP_real_real(plus_plus_real(X2),hAPP_real_real(times_times_real(X4),X0)) != hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_add__scale__eq__noteq) ).

fof(f416,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_nat_int(power_power_int(X0),X1)))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_zprime__zdvd__power) ).

fof(f417,axiom,
    zero_zero_int = number_number_of_int(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_semiring__norm_I112_J) ).

fof(f423,axiom,
    number267125858f_real(pls) = zero_zero_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_semiring__numeral__0__eq__0) ).

fof(f425,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_bin__less__0__simps_I1_J) ).

fof(f426,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),zero_zero_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_bin__less__0__simps_I3_J) ).

fof(f427,axiom,
    zero_zero_int = number_number_of_int(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_zero__is__num__zero) ).

fof(f428,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_int__0__less__1) ).

fof(f429,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0)))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_pos__zmult__pos) ).

fof(f433,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0))),hAPP_nat_nat(power_power_nat(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_power__Suc__less) ).

fof(f434,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0))),hAPP_nat_real(power_power_real(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_power__Suc__less) ).

fof(f435,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zprime,X3))
     => ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X2),X1)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left) ).

fof(f436,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zprime,X3))
     => ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X1),X2)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right) ).

fof(f437,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_sum__squares__ge__zero) ).

fof(f438,axiom,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_sum__squares__ge__zero) ).

fof(f439,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_sum__squares__le__zero__iff) ).

fof(f440,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real))
    <=> ( X1 = zero_zero_real
        & X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_sum__squares__le__zero__iff) ).

fof(f441,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_less__nat__number__of) ).

fof(f442,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_not__sum__squares__lt__zero) ).

fof(f443,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_not__sum__squares__lt__zero) ).

fof(f444,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_sum__squares__gt__zero__iff) ).

fof(f445,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))))
    <=> ( X1 != zero_zero_real
        | X0 != zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_sum__squares__gt__zero__iff) ).

fof(f446,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
    <=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_le__nat__number__of) ).

fof(f447,axiom,
    ! [X0] : number_number_of_int(bit0(X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X0))),number_number_of_int(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_number__of__Bit0) ).

fof(f449,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_power__one__right) ).

fof(f450,axiom,
    ! [X0] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_power__one__right) ).

fof(f451,axiom,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_power__one__right) ).

fof(f452,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_int__one__le__iff__zero__less) ).

fof(f453,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
       => ( hAPP_int_int(times_times_int(X1),X0) = one_one_int
        <=> ( X0 = one_one_int
            & X1 = one_one_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_pos__zmult__eq__1__iff) ).

fof(f454,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),zero_zero_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_odd__less__0) ).

fof(f455,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_less__special_I1_J) ).

fof(f456,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_less__special_I1_J) ).

fof(f457,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_less__special_I3_J) ).

fof(f458,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_less__special_I3_J) ).

fof(f459,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__special_I1_J) ).

fof(f460,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__special_I1_J) ).

fof(f461,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__special_I3_J) ).

fof(f462,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_le__special_I3_J) ).

fof(f463,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_le__imp__0__less) ).

fof(f469,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_zero__le__power2) ).

fof(f470,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_zero__le__power2) ).

fof(f471,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).

fof(f472,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_power2__le__imp__le) ).

fof(f473,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_power2__le__imp__le) ).

fof(f474,axiom,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
         => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).

fof(f475,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
         => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_power2__eq__imp__eq) ).

fof(f476,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
           => X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_power2__eq__imp__eq) ).

fof(f477,axiom,
    ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_power2__less__0) ).

fof(f478,axiom,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_power2__less__0) ).

fof(f479,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))))
    <=> X0 != zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_zero__less__power2) ).

fof(f480,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))))
      <=> X0 != zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_zero__less__power2) ).

fof(f482,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_sum__power2__eq__zero__iff) ).

fof(f486,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).

fof(f487,axiom,
    ! [X0,X1,X2] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_power__mult__distrib) ).

fof(f488,axiom,
    ! [X0,X1,X2] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_power__mult__distrib) ).

fof(f489,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_power__add) ).

fof(f490,axiom,
    ! [X0,X1,X2] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_power__add) ).

fof(f491,axiom,
    ! [X0,X1,X2] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_power__add) ).

fof(f492,axiom,
    ! [X0] : hAPP_nat_real(power_power_real(one_one_real),X0) = one_one_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_power__one) ).

fof(f494,axiom,
    ! [X0] : hAPP_nat_int(power_power_int(one_one_int),X0) = one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_power__one) ).

fof(f495,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_power__mult) ).

fof(f496,axiom,
    ! [X0,X1,X2] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_power__mult) ).

fof(f497,axiom,
    ! [X0,X1,X2] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_power__mult) ).

fof(f501,axiom,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_sum__power2__ge__zero) ).

fof(f502,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_sum__power2__ge__zero) ).

fof(f503,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
    <=> ( X1 = zero_zero_real
        & X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_sum__power2__le__zero__iff) ).

fof(f504,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_sum__power2__le__zero__iff) ).

fof(f505,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_not__sum__power2__lt__zero) ).

fof(f506,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_not__sum__power2__lt__zero) ).

fof(f507,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))))
    <=> ( X1 != zero_zero_real
        | X0 != zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_sum__power2__gt__zero__iff) ).

fof(f508,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_sum__power2__gt__zero__iff) ).

fof(f509,axiom,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_zero__le__even__power_H) ).

fof(f510,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_zero__le__even__power_H) ).

fof(f511,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_one__le__power) ).

fof(f512,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_one__le__power) ).

fof(f513,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_one__le__power) ).

fof(f514,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_power__increasing) ).

fof(f515,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_power__increasing) ).

fof(f516,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_power__increasing) ).

fof(f517,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
     => ( hAPP_nat_real(power_power_real(X2),X0) = hAPP_nat_real(power_power_real(X2),X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).

fof(f518,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
     => ( hAPP_nat_nat(power_power_nat(X2),X0) = hAPP_nat_nat(power_power_nat(X2),X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_power__inject__exp) ).

fof(f519,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
     => ( hAPP_nat_int(power_power_int(X2),X0) = hAPP_nat_int(power_power_int(X2),X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_power__inject__exp) ).

fof(f523,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).

fof(f524,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_power__less__imp__less__exp) ).

fof(f525,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_power__less__imp__less__exp) ).

fof(f526,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).

fof(f527,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_power__strict__increasing) ).

fof(f528,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_power__strict__increasing) ).

fof(f529,axiom,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_s) ).

fof(f530,axiom,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
     => ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),X1),X2))
       => ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_Euler_Oaux____1) ).

fof(f531,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(bit0(bit1(pls)))))
         => ( X0 = one_one_int
            | X0 = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_int__pos__lt__two__imp__zero__or__one) ).

fof(f532,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_real))
     => X0 = zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_even__power__le__0__imp__0) ).

fof(f533,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_int))
       => X0 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_even__power__le__0__imp__0) ).

fof(f534,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(zprime,X0))
      <=> ( ! [X1] :
              ( is_int(X1)
             => ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
                  & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
               => ( X1 = X0
                  | X1 = one_one_int ) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_zprime__def) ).

fof(f535,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( X2 = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_self__quotient__aux2) ).

fof(f536,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( X2 = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_self__quotient__aux1) ).

fof(f537,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(f538,axiom,
    ~ ! [X0] :
        ( is_int(X0)
       => ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).

fof(f539,axiom,
    legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)) = one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).

fof(f540,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
    <=> ( X1 = zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_nat__zero__less__power__iff) ).

fof(f541,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | X1 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_zero__less__power__nat__eq) ).

fof(f542,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | number_number_of_nat(X1) = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_zero__less__power__nat__eq__number__of) ).

fof(f543,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_nat__power__less__imp__less) ).

fof(f544,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( bit1(X0) = min
      <=> X0 = min ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_rel__simps_I47_J) ).

fof(f546,axiom,
    bit1(min) = min,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_Bit1__Min) ).

fof(f548,axiom,
    min != pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_rel__simps_I40_J) ).

fof(f550,axiom,
    ! [X0] : min != bit0(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_rel__simps_I42_J) ).

fof(f551,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_rel__simps_I7_J) ).

fof(f553,axiom,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
    <=> X0 = zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_not__real__square__gt__zero) ).

fof(f554,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),min))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_rel__simps_I13_J) ).

fof(f555,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_rel__simps_I9_J) ).

fof(f556,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_rel__simps_I3_J) ).

fof(f558,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_rel__simps_I8_J) ).

fof(f559,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_bin__less__0__simps_I2_J) ).

fof(f560,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),min))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_rel__simps_I30_J) ).

fof(f561,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_rel__simps_I26_J) ).

fof(f562,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_rel__simps_I20_J) ).

fof(f563,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_rel__simps_I23_J) ).

fof(f564,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),min))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_rel__simps_I28_J) ).

fof(f565,axiom,
    number_number_of_int(pls) != number_number_of_int(min),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_eq__number__of__Pls__Min) ).

fof(f566,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_power__dvd__imp__le) ).

fof(f568,axiom,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) = one_one_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(f570,axiom,
    ! [X0] : hAPP_nat_real(power_power_real(X0),zero_zero_nat) = one_one_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_power__0) ).

fof(f572,axiom,
    ! [X0] : hAPP_nat_int(power_power_int(X0),zero_zero_nat) = one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_power__0) ).

fof(f574,axiom,
    zero_zero_nat = number_number_of_nat(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_semiring__norm_I113_J) ).

fof(f575,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_rel__simps_I25_J) ).

fof(f576,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),min))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_rel__simps_I11_J) ).

fof(f577,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hAPP_int_int(times_times_int(X0),X1) = one_one_int
       => ( X0 = number_number_of_int(min)
          | X0 = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma) ).

fof(f578,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hAPP_int_int(times_times_int(X0),X1) = one_one_int
      <=> ( ( X1 = number_number_of_int(min)
            & X0 = number_number_of_int(min) )
          | ( X1 = one_one_int
            & X0 = one_one_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_zmult__eq__1__iff) ).

fof(f579,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_one__less__power) ).

fof(f580,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_one__less__power) ).

fof(f581,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_one__less__power) ).

fof(f582,axiom,
    ! [X0,X1] :
      ( ( X0 = one_one_real
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_nat_real(power_power_real(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_dvd__power) ).

fof(f583,axiom,
    ! [X0,X1] :
      ( ( X0 = one_one_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_dvd__power) ).

fof(f584,axiom,
    ! [X0,X1] :
      ( ( X0 = one_one_int
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_dvd__power) ).

fof(f585,axiom,
    ! [X0] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_less__0__number__of) ).

fof(f587,axiom,
    ! [X0] :
      ( zero_zero_nat = number_number_of_nat(X0)
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_eq__0__number__of) ).

fof(f588,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
    <=> hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_zcong__sym) ).

fof(f589,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_zcong__refl) ).

fof(f591,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_pos2) ).

fof(f592,axiom,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
       => hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(X2),X0))),X1) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
       => hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_nat__number__of__mult__left) ).

fof(f593,axiom,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
       => hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
       => hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_mult__nat__number__of) ).

fof(f599,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_IntPrimes_Ozcong__zero) ).

fof(f600,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_zcong__1) ).

fof(f601,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
       => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),X0),hAPP_int_int(times_times_int(X3),X1)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_zcong__zmult) ).

fof(f602,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X0),X2)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_zcong__scalar2) ).

fof(f603,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),hAPP_int_int(times_times_int(X2),X0)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_zcong__scalar) ).

fof(f604,axiom,
    ! [X0,X1,X2] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),X1)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_zcong__zmult__self) ).

fof(f605,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
       => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X2),X0),hAPP_int_int(plus_plus_int(X3),X1)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_zcong__zadd) ).

fof(f606,axiom,
    ! [X0] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)) = one_one_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_power__m1__even) ).

fof(f607,axiom,
    ! [X0] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)) = one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_power__m1__even) ).

fof(f608,axiom,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1)) = zero_zero_real
    <=> ( number_number_of_nat(X1) != zero_zero_nat
        & X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_power__eq__0__iff__number__of) ).

fof(f609,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)) = zero_zero_nat
    <=> ( number_number_of_nat(X1) != zero_zero_nat
        & X0 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_power__eq__0__iff__number__of) ).

fof(f610,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1)) = zero_zero_int
      <=> ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_power__eq__0__iff__number__of) ).

fof(f611,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(f613,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(f614,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
           => ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_zcong__not) ).

fof(f615,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(f616,axiom,
    ! [X0,X1,X2] :
      ( is_int(X1)
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      <=> ? [X3] :
            ( X1 = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3))
            & is_int(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_zcong__iff__lin) ).

fof(f617,axiom,
    ! [X0] :
      ( ( number_number_of_nat(X0) != zero_zero_nat
       => hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real )
      & ( number_number_of_nat(X0) = zero_zero_nat
       => hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_power__0__left__number__of) ).

fof(f618,axiom,
    ! [X0] :
      ( ( number_number_of_nat(X0) != zero_zero_nat
       => hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat )
      & ( number_number_of_nat(X0) = zero_zero_nat
       => hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_power__0__left__number__of) ).

fof(f619,axiom,
    ! [X0] :
      ( ( number_number_of_nat(X0) != zero_zero_nat
       => hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) = zero_zero_int )
      & ( number_number_of_nat(X0) = zero_zero_nat
       => hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_power__0__left__number__of) ).

fof(f620,axiom,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
             => ( hBOOL(hAPP_int_bool(zcong(X2,X0),X1))
               => X2 = X0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_zcong__zless__imp__eq) ).

fof(f622,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(f623,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),zero_zero_int))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
               => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_zdiv__mono2__neg__lemma) ).

fof(f624,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_unique__quotient__lemma__neg) ).

fof(f625,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
               => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_zdiv__mono2__lemma) ).

fof(f626,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_unique__quotient__lemma) ).

fof(f627,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_q__neg__lemma) ).

fof(f628,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_q__pos__lemma) ).

fof(f630,axiom,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),number_number_of_int(min))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).

fof(f632,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
     => ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2))
       => hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_neg__one__power__eq__mod__m) ).

fof(f633,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zcong(X0,number_number_of_int(min)),X1))
       => ~ hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1) ).

fof(f634,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X0))
     => ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_one__not__neg__one__mod__m) ).

fof(f635,axiom,
    hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).

fof(f636,axiom,
    ( ~ hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),number_number_of_int(min)))
   => legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)) != one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).

fof(f637,axiom,
    ! [X0,X1,X2] :
      ( is_int(X0)
     => ( hAPP_int_int(minus_minus_int(X0),X1) = X2
       => X0 = hAPP_int_int(plus_plus_int(X2),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_Int2_Oaux1) ).

fof(f638,axiom,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_real_real(minus_minus_real(number267125858f_real(X0)),number267125858f_real(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_number__of__diff) ).

fof(f639,axiom,
    ! [X0,X1] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),number_number_of_int(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_number__of__diff) ).

fof(f640,axiom,
    ! [X0] :
      ( is_int(X0)
     => hAPP_int_int(minus_minus_int(X0),pls) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_diff__bin__simps_I1_J) ).

fof(f642,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),X2)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_zdiff__zmult__distrib2) ).

fof(f643,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),X1)),X2) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_zdiff__zmult__distrib) ).

fof(f644,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
       => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X2),X0),hAPP_int_int(minus_minus_int(X3),X1)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_zcong__zdiff) ).

fof(f645,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_zdvd__zdiffD) ).

fof(f646,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(X1),X2)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(X0)),X1)),hAPP_real_real(times_times_real(number267125858f_real(X0)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_right__diff__distrib__number__of) ).

fof(f648,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X0),X1)),number267125858f_real(X2)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X0),number267125858f_real(X2))),hAPP_real_real(times_times_real(X1),number267125858f_real(X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_left__diff__distrib__number__of) ).

fof(f650,axiom,
    ! [X0,X1] : hAPP_int_int(minus_minus_int(bit1(X0)),bit0(X1)) = bit1(hAPP_int_int(minus_minus_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_diff__bin__simps_I9_J) ).

fof(f651,axiom,
    ! [X0,X1] : hAPP_int_int(minus_minus_int(bit1(X0)),bit1(X1)) = bit0(hAPP_int_int(minus_minus_int(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_diff__bin__simps_I10_J) ).

fof(f652,axiom,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),bit0(X0)) = bit0(hAPP_int_int(minus_minus_int(pls),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_diff__bin__simps_I3_J) ).

fof(f653,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__bin__lemma) ).

fof(f654,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X4),hAPP_int_int(times_times_int(X1),X5))),X6)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X4),X6))),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),hAPP_int_int(times_times_int(X5),X6)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_xzgcda__linear__aux1) ).

fof(f655,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_zcong__def) ).

fof(f656,axiom,
    ! [X0,X1,X2] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_add__number__of__diff1) ).

fof(f657,axiom,
    ! [X0,X1,X2] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_add__number__of__diff1) ).

fof(f658,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
         => ( X1 != hAPP_int_int(minus_minus_int(X0),one_one_int)
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_Euler_Oaux1) ).

fof(f659,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_zle__diff1__eq) ).

fof(f660,axiom,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),bit1(X0)) = bit1(hAPP_int_int(minus_minus_int(min),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_diff__bin__simps_I4_J) ).

fof(f661,axiom,
    ! [X0] : hAPP_int_int(minus_minus_int(min),bit0(X0)) = bit1(hAPP_int_int(minus_minus_int(min),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_diff__bin__simps_I5_J) ).

fof(f662,axiom,
    ! [X0] : hAPP_int_int(minus_minus_int(min),bit1(X0)) = bit0(hAPP_int_int(minus_minus_int(min),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_diff__bin__simps_I6_J) ).

fof(f663,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1))
    <=> hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_inv__not__p__minus__1__aux) ).

fof(f664,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( X3 = X1
       => ( hBOOL(hAPP_int_bool(zcong(X1,X0),X4))
         => hBOOL(hAPP_int_bool(zcong(X2,X0),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_zcong__eq__trans) ).

fof(f665,axiom,
    ! [X0,X1,X2,X3] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))),twoSqu1241645765sum2sq(product_Pair_int_int(X2,X3))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X1),X2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_mult__sum2sq) ).

fof(f666,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
       => ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
         => ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
            | hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_zcong__square) ).

fof(f667,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
           => ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
             => ( X0 = hAPP_int_int(minus_minus_int(X1),one_one_int)
                | X0 = one_one_int ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_zcong__square__zless) ).

fof(f668,axiom,
    ! [X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_zspecial__product) ).

fof(f669,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_zcong__id) ).

fof(f670,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4))
      <=> hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_zcong__zmult__prop1) ).

fof(f671,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
     => ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4))
      <=> hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_zcong__zmult__prop2) ).

fof(f672,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X1),X0),hAPP_int_int(plus_plus_int(X2),X0)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_zcong__shift) ).

fof(f673,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X0),hAPP_nat_int(power_power_int(X2),X0)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_zcong__zpower) ).

fof(f674,axiom,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_power2__diff) ).

fof(f675,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_power2__diff) ).

fof(f676,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_zdiff__power2) ).

fof(f677,axiom,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit1(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_zdiff__power3) ).

fof(f678,axiom,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X1) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
           => ( hBOOL(hAPP_int_bool(zcong(X2,X1),X0))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
               => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
                 => X2 = X1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zcong__less__eq) ).

fof(f679,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
       => ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_zcong__not__zero) ).

fof(f680,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_zdvd__bounds) ).

fof(f682,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_zcong__zero__equiv__div) ).

fof(f683,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(X0),X1)))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_zprime__zdvd__zmult__better) ).

fof(f684,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
         => ( hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0))
           => X1 = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_Int2_Ozcong__zero) ).

fof(f685,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_zpower__zdvd__prop1) ).

fof(f686,axiom,
    ! [X0] :
      ( hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = number_number_of_int(min)
      | hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_neg__one__power) ).

fof(f687,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
         => ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),zero_zero_int),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_zcong__zmult__prop3) ).

fof(f691,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)))
     => legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)) = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_Legendre__1mod4) ).

fof(f692,axiom,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
       => ( ( ~ hBOOL(hAPP_int_bool(quadRes(X1),X0))
           => legendre(X0,X1) = number_number_of_int(min) )
          & ( hBOOL(hAPP_int_bool(quadRes(X1),X0))
           => legendre(X0,X1) = one_one_int ) ) )
      & ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
       => legendre(X0,X1) = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_Legendre__def) ).

fof(f693,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1))
        | X1 = X0
        | X1 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_divides__cases) ).

fof(f694,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(quadRes(X0),X1))
    <=> ? [X2] :
          ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
          & is_int(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_QuadRes__def) ).

fof(f695,axiom,
    ! [X0,X1] :
      ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
    <=> ( X1 = zero_zero_real
        & X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_realpow__two__sum__zero__iff) ).

fof(f696,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
         => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
           => ( hAPP_real_real(plus_plus_real(X1),X0) = one_one_real
             => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X3)),hAPP_real_real(times_times_real(X0),X2))),X4)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_convex__bound__lt) ).

fof(f697,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
           => ( hAPP_int_int(plus_plus_int(X1),X0) = one_one_int
             => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(times_times_int(X0),X2))),X4)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_convex__bound__lt) ).

fof(f698,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),zero_zero_real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_dvd__0__right) ).

fof(f700,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_dvd__0__right) ).

fof(f701,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
    <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_real__le__eq__diff) ).

fof(f702,axiom,
    ! [X0,X1] :
      ( X0 != X1
     => ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_linorder__neqE__linordered__idom) ).

fof(f704,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_dvd__refl) ).

fof(f706,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_dvd__refl) ).

fof(f707,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_dvd__trans) ).

fof(f709,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_dvd__trans) ).

fof(f712,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
    <=> ( X0 != X1
        & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_real__less__def) ).

fof(f714,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_real__mult__assoc) ).

fof(f715,axiom,
    ! [X0,X1] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_real__mult__commute) ).

fof(f716,axiom,
    ! [X0] : hAPP_real_real(times_times_real(one_one_real),X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_real__mult__1) ).

fof(f717,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_real__add__left__mono) ).

fof(f718,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_nat(power_power_nat(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_realpow__minus__mult) ).

fof(f719,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_real(power_power_real(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_realpow__minus__mult) ).

fof(f720,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_int(power_power_int(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_realpow__minus__mult) ).

fof(f721,axiom,
    ! [X0,X1] :
      ( ( X1 != zero_zero_nat
       => hAPP_nat_nat(times_times_nat(X1),X0) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),one_one_nat)),X0)) )
      & ( X1 = zero_zero_nat
       => hAPP_nat_nat(times_times_nat(X1),X0) = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_mult__eq__if) ).

fof(f722,axiom,
    ! [X0,X1] :
      ( ( X1 != zero_zero_nat
       => hAPP_nat_nat(power_power_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))) )
      & ( X1 = zero_zero_nat
       => hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_power__eq__if) ).

fof(f723,axiom,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_diff__square) ).

fof(f730,axiom,
    ! [X0,X1] :
      ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real
    <=> ( X1 = zero_zero_real
        | X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_mult__eq__0__iff) ).

fof(f731,axiom,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hAPP_int_int(times_times_int(X0),X1) = zero_zero_int
      <=> ( X1 = zero_zero_int
          | X0 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_mult__eq__0__iff) ).

fof(f732,axiom,
    ! [X0] : hAPP_real_real(times_times_real(X0),zero_zero_real) = zero_zero_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_mult__zero__right) ).

fof(f734,axiom,
    ! [X0] : hAPP_int_int(times_times_int(X0),zero_zero_int) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_mult__zero__right) ).

fof(f735,axiom,
    ! [X0] : hAPP_real_real(times_times_real(zero_zero_real),X0) = zero_zero_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_mult__zero__left) ).

fof(f737,axiom,
    ! [X0] : hAPP_int_int(times_times_int(zero_zero_int),X0) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_mult__zero__left) ).

fof(f741,axiom,
    one_one_real != zero_zero_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_one__neq__zero) ).

fof(f742,axiom,
    one_one_nat != zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_one__neq__zero) ).

fof(f743,axiom,
    one_one_int != zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_one__neq__zero) ).

fof(f744,axiom,
    ! [X0,X1,X2,X3] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X2)),X1)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_combine__common__factor) ).

fof(f745,axiom,
    ! [X0,X1,X2,X3] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_combine__common__factor) ).

fof(f746,axiom,
    ! [X0,X1,X2,X3] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X2)),X1)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_combine__common__factor) ).

fof(f749,axiom,
    ! [X0,X1,X2] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_comm__semiring__class_Odistrib) ).

fof(f750,axiom,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0))
     => X0 = zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_dvd__0__left) ).

fof(f752,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),X0))
       => X0 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_dvd__0__left) ).

fof(f753,axiom,
    ! [X0,X1,X2,X3] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(X0),X2)),hAPP_real_real(minus_minus_real(X1),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_add__diff__add) ).

fof(f754,axiom,
    ! [X0,X1,X2,X3] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X2)),hAPP_int_int(minus_minus_int(X1),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_add__diff__add) ).

fof(f755,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_dvd__mult__right) ).

fof(f756,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_dvd__mult__right) ).

fof(f757,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_dvd__mult__right) ).

fof(f758,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_dvd__mult__left) ).

fof(f759,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_dvd__mult__left) ).

fof(f760,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_dvd__mult__left) ).

fof(f764,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_mult__dvd__mono) ).

fof(f765,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_mult__dvd__mono) ).

fof(f766,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_mult__dvd__mono) ).

fof(f767,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_dvd__mult) ).

fof(f768,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_dvd__mult) ).

fof(f769,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_dvd__mult) ).

fof(f770,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_dvd__mult2) ).

fof(f771,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_dvd__mult2) ).

fof(f772,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_dvd__mult2) ).

fof(f773,axiom,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_dvd__triv__right) ).

fof(f774,axiom,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_dvd__triv__right) ).

fof(f775,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_dvd__triv__right) ).

fof(f776,axiom,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X0),X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_dvd__triv__left) ).

fof(f777,axiom,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X0),X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_dvd__triv__left) ).

fof(f778,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X0),X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_dvd__triv__left) ).

fof(f779,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(plus_plus_real(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_dvd__add) ).

fof(f780,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_dvd__add) ).

fof(f781,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(plus_plus_int(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_dvd__add) ).

fof(f782,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_one__dvd) ).

fof(f784,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_one__dvd) ).

fof(f785,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(minus_minus_real(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_dvd__diff) ).

fof(f786,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_dvd__diff) ).

fof(f787,axiom,
    ! [X0,X1,X2] :
      ( X2 != zero_zero_real
     => ( hAPP_real_real(times_times_real(X0),X2) = hAPP_real_real(times_times_real(X1),X2)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_real__mult__right__cancel) ).

fof(f788,axiom,
    ! [X0,X1,X2] :
      ( X2 != zero_zero_real
     => ( hAPP_real_real(times_times_real(X2),X0) = hAPP_real_real(times_times_real(X2),X1)
      <=> X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_real__mult__left__cancel) ).

fof(f789,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_divides__add__revr) ).

fof(f793,axiom,
    ! [X0,X1,X2] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_real__add__mult__distrib) ).

fof(f794,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) = zero_zero_nat
    <=> ( X0 = zero_zero_nat
        & X1 != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_nat__power__eq__0__iff) ).

fof(f795,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_divides__exp) ).

fof(f797,axiom,
    ! [X0,X1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) )
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_split__mult__neg__le) ).

fof(f798,axiom,
    ! [X0,X1] :
      ( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_split__mult__neg__le) ).

fof(f801,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
         => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
           => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_mult__mono) ).

fof(f803,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_mult__mono) ).

fof(f804,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
       => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
         => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
           => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_mult__mono_H) ).

fof(f806,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_mult__mono_H) ).

fof(f807,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X0),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_mult__left__mono__neg) ).

fof(f808,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X0),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_mult__left__mono__neg) ).

fof(f809,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_mult__right__mono__neg) ).

fof(f810,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_mult__right__mono__neg) ).

fof(f813,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_comm__mult__left__mono) ).

fof(f814,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_mult__left__mono) ).

fof(f817,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X0)),hAPP_real_real(times_times_real(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_mult__right__mono) ).

fof(f819,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_mult__right__mono) ).

fof(f834,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
    <=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_mult__le__0__iff) ).

fof(f835,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int))
    <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_mult__le__0__iff) ).

fof(f836,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
    <=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_zero__le__mult__iff) ).

fof(f837,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
    <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_zero__le__mult__iff) ).

fof(f838,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_zero__le__square) ).

fof(f839,axiom,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_zero__le__square) ).

fof(f853,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_mult__neg__neg) ).

fof(f854,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_mult__neg__neg) ).

fof(f857,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_mult__neg__pos) ).

fof(f858,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_mult__less__cancel__left__neg) ).

fof(f859,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_mult__less__cancel__left__neg) ).

fof(f860,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_zero__less__mult__pos2) ).

fof(f862,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_zero__less__mult__pos2) ).

fof(f863,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_zero__less__mult__pos) ).

fof(f866,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_mult__pos__neg2) ).

fof(f869,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_mult__pos__neg) ).

fof(f871,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_mult__pos__neg) ).

fof(f874,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_mult__pos__pos) ).

fof(f875,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_mult__less__cancel__left__pos) ).

fof(f876,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_mult__less__cancel__left__pos) ).

fof(f877,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
    <=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_mult__less__cancel__left__disj) ).

fof(f878,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
    <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_mult__less__cancel__left__disj) ).

fof(f879,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
    <=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_mult__less__cancel__right__disj) ).

fof(f880,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
    <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_mult__less__cancel__right__disj) ).

fof(f881,axiom,
    ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X0)),zero_zero_real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_not__square__less__zero) ).

fof(f882,axiom,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X0)),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_not__square__less__zero) ).

fof(f884,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_pos__add__strict) ).

fof(f886,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
        | X1 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H) ).

fof(f887,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_real__mult__less__iff1) ).

fof(f888,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_real__mult__le__cancel__iff1) ).

fof(f889,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_real__mult__le__cancel__iff2) ).

fof(f890,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_real__mult__order) ).

fof(f891,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_real__mult__less__mono2) ).

fof(f892,axiom,
    ! [X0,X1] :
      ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) = zero_zero_real
    <=> ( X1 = zero_zero_real
        & X0 = zero_zero_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_real__two__squares__add__zero__iff) ).

fof(f893,axiom,
    ! [X0,X1,X2] :
      ( X2 != zero_zero_nat
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_divides__exp2) ).

fof(f895,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat
    <=> ( X1 = zero_zero_nat
        | X0 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_exp__eq__1) ).

fof(f896,axiom,
    ! [X0,X1,X2,X3] :
      ( X0 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3)
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_divides__div__not) ).

fof(f897,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_two__realpow__ge__one) ).

fof(f898,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
       => ? [X2] :
            ( hAPP_nat_real(power_power_real(X2),X1) = X0
            & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_realpow__pos__nth) ).

fof(f899,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
       => ? [X2] :
            ( ! [X3] :
                ( ( hAPP_nat_real(power_power_real(X3),X1) = X0
                  & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) )
               => X3 = X2 )
            & hAPP_nat_real(power_power_real(X2),X1) = X0
            & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_realpow__pos__nth__unique) ).

fof(f900,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1))
      <=> X0 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_dvd__mult__cancel2) ).

fof(f901,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X0)),X1))
      <=> X0 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_dvd__mult__cancel1) ).

fof(f902,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_le0) ).

fof(f905,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_diff__commute) ).

fof(f906,axiom,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_real__le__refl) ).

fof(f907,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_real__le__linear) ).

fof(f908,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X0))
       => hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_real__le__trans) ).

fof(f909,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
     => ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_real__le__antisym) ).

fof(f910,axiom,
    ! [X0] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_diff__0__eq__0) ).

fof(f911,axiom,
    ! [X0] : hAPP_nat_nat(minus_minus_nat(X0),zero_zero_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_minus__nat_Odiff__0) ).

fof(f912,axiom,
    ! [X0] : hAPP_nat_nat(minus_minus_nat(X0),X0) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_diff__self__eq__0) ).

fof(f913,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat
     => ( hAPP_nat_nat(minus_minus_nat(X1),X0) = zero_zero_nat
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_diffs0__imp__equal) ).

fof(f919,axiom,
    ! [X0,X1] :
      ( X0 != X1
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_nat__neq__iff) ).

fof(f921,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_diff__less__mono2) ).

fof(f922,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_less__imp__diff__less) ).

fof(f937,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_dvd_Oorder__trans) ).

fof(f950,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_dvd_Oeq__iff) ).

fof(f952,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(minus_minus_nat(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_dvd__diff__nat) ).

fof(f953,axiom,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_nat__add__commute) ).

fof(f954,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_nat__add__left__commute) ).

fof(f955,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_nat__add__assoc) ).

fof(f956,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X0),X2)
    <=> X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_nat__add__left__cancel) ).

fof(f957,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X2),X1)
    <=> X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_nat__add__right__cancel) ).

fof(f958,axiom,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_diff__add__inverse2) ).

fof(f959,axiom,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_diff__add__inverse) ).

fof(f960,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_diff__diff__left) ).

fof(f961,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_Nat_Odiff__cancel) ).

fof(f962,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_diff__cancel2) ).

fof(f964,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_nat__le__linear) ).

fof(f966,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_le__trans) ).

fof(f968,axiom,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_Nat_Odiff__le__self) ).

fof(f969,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_diff__le__mono2) ).

fof(f970,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_diff__le__mono) ).

fof(f971,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_diff__diff__cancel) ).

fof(f972,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
       => ( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1)
        <=> X2 = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_eq__diff__iff) ).

fof(f973,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
       => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(X2),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_Nat_Odiff__diff__eq) ).

fof(f974,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_le__diff__iff) ).

fof(f975,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_nat__mult__assoc) ).

fof(f976,axiom,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_nat__mult__commute) ).

fof(f977,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_diff__mult__distrib) ).

fof(f978,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_diff__mult__distrib2) ).

fof(f982,axiom,
    ! [X0] :
      ( X0 != zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_neq0__conv) ).

fof(f983,axiom,
    ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_not__less0) ).

fof(f984,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_diff__less) ).

fof(f985,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_zero__less__diff) ).

fof(f986,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X0
     => X1 = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_add__eq__self__zero) ).

fof(f987,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) = zero_zero_nat
    <=> ( X1 = zero_zero_nat
        & X0 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_add__is__0) ).

fof(f988,axiom,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_Nat_Oadd__0__right) ).

fof(f989,axiom,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_plus__nat_Oadd__0) ).

fof(f990,axiom,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X0),X1)) = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_diff__add__0) ).

fof(f991,axiom,
    ! [X0] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
    <=> X0 = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_le__0__eq) ).

fof(f992,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_less__eq__nat_Osimps_I1_J) ).

fof(f994,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_diff__is__0__eq) ).

fof(f997,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat
    <=> ( X1 = zero_zero_nat
        | X0 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_mult__is__0) ).

fof(f999,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X2),X1)
    <=> ( X1 = zero_zero_nat
        | X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_mult__cancel2) ).

fof(f1000,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_not__add__less1) ).

fof(f1001,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_not__add__less2) ).

fof(f1002,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_nat__add__left__cancel__less) ).

fof(f1003,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_trans__less__add1) ).

fof(f1004,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_trans__less__add2) ).

fof(f1005,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_add__less__mono1) ).

fof(f1006,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_add__less__mono) ).

fof(f1007,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
     => ( hAPP_nat_nat(plus_plus_nat(X0),X3) = hAPP_nat_nat(plus_plus_nat(X2),X1)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_less__add__eq__less) ).

fof(f1008,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_add__lessD1) ).

fof(f1009,axiom,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_add__diff__inverse) ).

fof(f1010,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_less__diff__conv) ).

fof(f1011,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
    <=> ( X0 != X1
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_nat__less__le) ).

fof(f1014,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( X0 != X1
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_le__neq__implies__less) ).

fof(f1015,axiom,
    ! [X0,X1] :
      ( ( X0 = X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_less__or__eq__imp__le) ).

fof(f1016,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_less__diff__iff) ).

fof(f1017,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_diff__less__mono) ).

fof(f1018,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_dvd__reduce) ).

fof(f1019,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_dvd__diffD1) ).

fof(f1020,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_dvd__diffD) ).

fof(f1021,axiom,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_le__add2) ).

fof(f1023,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
    <=> ? [X2] : X1 = hAPP_nat_nat(plus_plus_nat(X0),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_le__iff__add) ).

fof(f1024,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_nat__add__left__cancel__le) ).

fof(f1025,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_trans__le__add1) ).

fof(f1026,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_trans__le__add2) ).

fof(f1027,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_add__le__mono1) ).

fof(f1028,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_add__le__mono) ).

fof(f1031,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_add__leE) ).

fof(f1032,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_diff__diff__right) ).

fof(f1033,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_le__diff__conv) ).

fof(f1034,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_le__add__diff) ).

fof(f1035,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_le__add__diff__inverse) ).

fof(f1037,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_le__diff__conv2) ).

fof(f1040,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_diff__add__assoc) ).

fof(f1042,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_diff__add__assoc2) ).

fof(f1043,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_add__mult__distrib) ).

fof(f1044,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_add__mult__distrib2) ).

fof(f1046,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_mult__le__mono) ).

fof(f1049,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_le__cube) ).

fof(f1050,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_le__square) ).

fof(f1052,axiom,
    ! [X0] : hAPP_nat_nat(times_times_nat(X0),one_one_nat) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_nat__mult__1__right) ).

fof(f1053,axiom,
    ! [X0,X1] :
      ( one_one_nat = hAPP_nat_nat(times_times_nat(X0),X1)
    <=> ( X1 = one_one_nat
        & X0 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_nat__1__eq__mult__iff) ).

fof(f1054,axiom,
    ! [X0] : hAPP_nat_nat(times_times_nat(one_one_nat),X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_nat__mult__1) ).

fof(f1055,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
       => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_nat__dvd__not__less) ).

fof(f1056,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_add__gr__0) ).

fof(f1057,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
    <=> ( ! [X3] :
            ( X1 = hAPP_nat_nat(plus_plus_nat(X2),X3)
           => hBOOL(hAPP_nat_bool(X0,X3)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
         => hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_nat__diff__split) ).

fof(f1058,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
    <=> ~ ( ? [X3] :
              ( ~ hBOOL(hAPP_nat_bool(X0,X3))
              & X1 = hAPP_nat_nat(plus_plus_nat(X2),X3) )
          | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_nat__diff__split__asm) ).

fof(f1061,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_mult__less__cancel2) ).

fof(f1062,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_mult__less__cancel1) ).

fof(f1063,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_nat__0__less__mult__iff) ).

fof(f1064,axiom,
    ! [X0,X1] :
      ( X0 = hAPP_nat_nat(times_times_nat(X0),X1)
     => ( X0 = zero_zero_nat
        | X1 = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_mult__eq__self__implies__10) ).

fof(f1065,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_dvd__imp__le) ).

fof(f1067,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_mult__le__cancel1) ).

fof(f1068,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_mult__le__cancel2) ).

fof(f1069,axiom,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X1,X0))
       => ? [X2] :
            ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(X2),one_one_nat)))
            & ! [X3] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
               => ~ hBOOL(hAPP_nat_bool(X1,X3)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_ex__least__nat__less) ).

fof(f1070,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_nat__less__add__iff2) ).

fof(f1071,axiom,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),X2)
    <=> ( X1 = X2
        | X0 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_nat__mult__eq__cancel__disj) ).

fof(f1072,axiom,
    ! [X0,X1,X2,X3] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_left__add__mult__distrib) ).

fof(f1074,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_nat__mult__less__cancel1) ).

fof(f1075,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
        | X0 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj) ).

fof(f1076,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_nat__mult__dvd__cancel1) ).

fof(f1077,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_nat__mult__le__cancel1) ).

fof(f1078,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_nat__le__add__iff1) ).

fof(f1079,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_nat__diff__add__eq1) ).

fof(f1080,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)
      <=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_nat__eq__add__iff1) ).

fof(f1081,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_nat__le__add__iff2) ).

fof(f1082,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_nat__diff__add__eq2) ).

fof(f1083,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)
      <=> X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_nat__eq__add__iff2) ).

fof(f1084,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_nat__less__add__iff1) ).

fof(f1085,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X0))))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X0)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_number__of1) ).

fof(f1086,axiom,
    ! [X0] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      <=> ? [X1,X2] :
            ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) = X0
            & is_int(X2)
            & is_int(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_is__sum2sq__def) ).

fof(f1089,axiom,
    ! [X0,X1,X2] :
      ( is_int(X2)
     => ( X2 != zero_zero_int
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
        <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_zdvd__mono) ).

fof(f1091,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( ! [X3] :
            ( is_int(X3)
           => ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),X2))) ) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ! [X3] :
              ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_decr__mult__lemma) ).

fof(f1092,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( ! [X3] :
            ( is_int(X3)
           => ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),X2))) ) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ! [X3] :
              ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_incr__mult__lemma) ).

fof(f1093,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
     => ? [X1] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
          & hBOOL(hAPP_int_bool(zprime,X1))
          & is_int(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_zprime__factor__exists) ).

fof(f1094,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ? [X2] :
          ( ! [X3] :
              ( is_int(X3)
             => ( ( hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
                  & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
                  & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
               => X3 = X2 ) )
          & hBOOL(hAPP_int_bool(zcong(X0,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          & is_int(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_zcong__zless__unique) ).

fof(f1095,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_norR__mem__unique__aux) ).

fof(f1096,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
     => hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),number_number_of_int(min)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_Wilson__Russ) ).

fof(f1097,axiom,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
       => zfact(X0) = hAPP_int_int(times_times_int(X0),zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
       => zfact(X0) = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_zfact_Osimps) ).

fof(f1098,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X1))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
             => inv(X1,inv(X1,X0)) = X0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_inv__inv) ).

fof(f1099,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
         => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
           => ( ~ hBOOL(hAPP_int_bool(quadRes(X2),X1))
             => ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_MultInvPair__distinct) ).

fof(f1100,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3))
     => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X0)),X0)),X1),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_aux______3) ).

fof(f1102,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => X0 != inv(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_inv__distinct) ).

fof(f1103,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => inv(X1,X0) != one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_inv__not__1) ).

fof(f1104,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => inv(X1,X0) != hAPP_int_int(minus_minus_int(X1),one_one_int) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_inv__not__p__minus__1) ).

fof(f1105,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(X1,X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_inv__g__1) ).

fof(f1106,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(X1,X0)),hAPP_int_int(minus_minus_int(X1),one_one_int))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_inv__less__p__minus__1) ).

fof(f1107,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
     => ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
       => hBOOL(hAPP_int_bool(zcong(multInv(X2,X0),multInv(X2,X1)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_MultInv__prop1) ).

fof(f1108,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
         => inv(X1,X0) != zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_inv__not__0) ).

fof(f1109,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
     => ( hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
       => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X3,X1)),hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_MultInv__zcong__prop1) ).

fof(f1110,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
     => ( hBOOL(hAPP_int_bool(zprime,X2))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
         => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
           => ( hBOOL(hAPP_int_bool(zcong(multInv(X2,X1),multInv(X2,X0)),X2))
             => hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_MultInv__prop5) ).

fof(f1111,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
         => hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),X0),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_MultInv__prop4) ).

fof(f1112,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
         => ~ hBOOL(hAPP_int_bool(zcong(multInv(X1,X0),zero_zero_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_MultInv__prop3) ).

fof(f1113,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zprime,X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
         => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_inv__is__inv) ).

fof(f1114,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
     => ( hBOOL(hAPP_int_bool(zprime,X3))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
         => ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X2)),X2)),X0),hAPP_int_int(times_times_int(multInv(X3,X2)),X1)),X3))
           => hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_aux______4) ).

fof(f1115,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
     => ( hBOOL(hAPP_int_bool(zprime,X3))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
         => ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X2)),X3))
           => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),X1),X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_aux______2) ).

fof(f1116,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
     => ( hBOOL(hAPP_int_bool(zprime,X3))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
         => ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
           => ( hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3))
             => hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X0),multInv(X3,X1))),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_MultInv__zcong__prop2) ).

fof(f1117,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
     => ( hBOOL(hAPP_int_bool(zprime,X3))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
         => ( ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
           => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X3))
             => ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),multInv(X3,X0)),hAPP_int_int(times_times_int(X2),multInv(X3,X1))),X3))
               => hBOOL(hAPP_int_bool(zcong(X0,X1),X3)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_MultInv__zcong__prop3) ).

fof(f1118,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
         => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0))),X0),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_Int2_Oaux____2) ).

fof(f1119,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
         => hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0)))),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_Int2_Oaux____1) ).

fof(f1121,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
     => ( hBOOL(hAPP_int_bool(zprime,X1))
       => ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
         => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X0)),one_one_int),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_MultInv__prop2) ).

fof(f1122,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
         => ( hBOOL(member_int(X0,wset(X1,X2)))
           => hBOOL(member_int(inv(X2,X0),wset(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_wset__mem__inv__mem) ).

fof(f1123,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int)))
             => ( hBOOL(member_int(inv(X2,X0),wset(X1,X2)))
               => hBOOL(member_int(X0,wset(X1,X2))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_wset__inv__mem__mem) ).

fof(f1124,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
     => hBOOL(member_int(X1,wset(X1,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_wset__mem__mem) ).

fof(f1125,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
     => ( hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
       => hBOOL(member_int(X0,wset(X2,X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_wset__subset) ).

fof(f1126,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
       => ( hBOOL(member_int(X0,wset(X1,X2)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_wset__less) ).

fof(f1127,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
       => ( hBOOL(member_int(X0,wset(X1,X2)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_wset__g__1) ).

fof(f1128,axiom,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
       => ( ~ hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
         => ( hBOOL(member_int(X0,wset(X2,X1)))
           => ( X0 = inv(X1,X2)
              | X0 = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_wset__mem__imp__or) ).

fof(f1129,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zprime,X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
           => hBOOL(member_int(X0,wset(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_wset__mem) ).

fof(f1130,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,X2))
       => ( ! [X3] :
              ( is_int(X3)
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
               => ( hBOOL(hAPP_int_bool(X0,X3))
                 => hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) ) ) )
         => hBOOL(hAPP_int_bool(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_int__le__induct) ).

fof(f1131,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
       => ( ! [X3] :
              ( is_int(X3)
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
               => ( hBOOL(hAPP_int_bool(X0,X3))
                 => hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) ) ) )
         => hBOOL(hAPP_int_bool(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_int__less__induct) ).

fof(f1132,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( is_int(X2)
         => ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X2),one_one_int))) )
           => hBOOL(hAPP_int_bool(X1,X2)) ) )
     => hBOOL(hAPP_int_bool(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_d22set__induct__old) ).

fof(f1133,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,X1))
       => ( ! [X3] :
              ( is_int(X3)
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
               => ( hBOOL(hAPP_int_bool(X0,X3))
                 => hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) ) ) )
         => hBOOL(hAPP_int_bool(X0,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_int__ge__induct) ).

fof(f1134,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
       => ( ! [X3] :
              ( is_int(X3)
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
               => ( hBOOL(hAPP_int_bool(X0,X3))
                 => hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) ) ) )
         => hBOOL(hAPP_int_bool(X0,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_int__gr__induct) ).

fof(f1135,axiom,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,X4))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X2,X0)),X1)),hAPP_nat_nat(X2,hAPP_nat_nat(plus_plus_nat(X0),X1)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_mono__nat__linear__lb) ).

fof(f1136,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
     => d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls)))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_d22set__eq__wset) ).

fof(f1137,axiom,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X1,X0))
       => ? [X2] :
            ( hBOOL(hAPP_nat_bool(X1,X2))
            & ! [X3] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
               => ~ hBOOL(hAPP_nat_bool(X1,X3)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_ex__least__nat__le) ).

fof(f1139,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
     => ~ hBOOL(member_int(X1,d22set(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_d22set__le__swap) ).

fof(f1140,axiom,
    ! [X0,X1] :
      ( hBOOL(member_int(X0,d22set(X1)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_d22set__g__1) ).

fof(f1141,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
       => hBOOL(member_int(X1,d22set(X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_d22set__mem) ).

fof(f1142,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ? [X2] :
          ( hAPP_nat_nat(plus_plus_nat(X0),X2) = X1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_less__imp__add__positive) ).

fof(f1146,axiom,
    ! [X0] :
      ( X0 != zero_zero_nat
    <=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top) ).

fof(f1147,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

fof(f1150,axiom,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least) ).

fof(f1153,axiom,
    ! [X0] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
     => X0 = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot) ).

fof(f1154,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_dvd__pos__nat) ).

fof(f1155,axiom,
    ! [X0,X1,X2] :
      ( X2 != zero_zero_nat
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_pow__divides__eq__nat) ).

fof(f1156,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
     => ( X1 != zero_zero_nat
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_pow__divides__pow__int) ).

fof(f1157,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
     => ( X1 = zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_divides__le) ).

fof(f1158,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( hAPP_nat_nat(times_times_nat(X2),X0) = hAPP_nat_nat(times_times_nat(X2),X1)
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_mult__left__cancel) ).

fof(f1159,axiom,
    ! [X0] : sr(X0) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),cOMBC_int_int_bool(ord_less_int,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_SR__def) ).

fof(f1160,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
     => hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))),one_one_int) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_neg__zmod__mult__2) ).

fof(f1161,axiom,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
       => hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
       => hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1)))),one_one_int) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_zmod__number__of__Bit1) ).

fof(f1162,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1)))
    <=> hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)) = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of) ).

fof(f1165,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X1),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(f1166,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_zmod__le__nonneg__dividend) ).

fof(f1167,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int
      <=> ? [X2] :
            ( X0 = hAPP_int_int(times_times_int(X1),X2)
            & is_int(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_zmod__eq__0__iff) ).

fof(f1168,axiom,
    ! [X0,X1,X2] :
      ( hAPP_int_int(div_mod_int(X0),X1) = hAPP_int_int(div_mod_int(X2),X1)
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_zmod__eq__dvd__iff) ).

fof(f1169,axiom,
    ! [X0,X1,X2] :
      ( hAPP_int_int(div_mod_int(X0),X1) = hAPP_int_int(div_mod_int(X2),X1)
     => hBOOL(hAPP_int_bool(zcong(X0,X2),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_Residues_Oaux) ).

fof(f1171,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
    <=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_zcong__zmod) ).

fof(f1172,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X1),X2)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd) ).

fof(f1173,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(div_mod_int(X2),X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_zdvd__zmod) ).

fof(f1174,axiom,
    ! [X0,X1,X2] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(X0),X2)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_zpower__zmod) ).

fof(f1176,axiom,
    ! [X0,X1,X2] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_zmod__simps_I3_J) ).

fof(f1177,axiom,
    ! [X0] : hAPP_int_int(div_mod_int(X0),X0) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_zmod__self) ).

fof(f1178,axiom,
    ! [X0] : hAPP_int_int(div_mod_int(zero_zero_int),X0) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_zmod__zero) ).

fof(f1179,axiom,
    ! [X0,X1,X2] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X1)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_zdiff__zmod__right) ).

fof(f1180,axiom,
    ! [X0,X1,X2] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X2)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_zdiff__zmod__left) ).

fof(f1181,axiom,
    ! [X0] : hAPP_int_int(div_mod_int(X0),number_number_of_int(min)) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_zmod__minus1__right) ).

fof(f1182,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
       => hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X0),X1)),X2) = hAPP_int_int(div_mod_int(X0),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_zmod__zdvd__zmod) ).

fof(f1186,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
         => hAPP_int_int(div_mod_int(X1),X0) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_mod__pos__pos__trivial) ).

fof(f1188,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(div_mod_int(X0),X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),zero_zero_int)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_neg__mod__conj) ).

fof(f1189,axiom,
    ! [X0,X1] :
      ( is_int(X1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
         => hAPP_int_int(div_mod_int(X1),X0) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_mod__neg__neg__trivial) ).

fof(f1190,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X0)),zero_zero_int))
       => hAPP_int_int(div_mod_int(X1),X0) = hAPP_int_int(plus_plus_int(X1),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_mod__pos__neg__trivial) ).

fof(f1191,axiom,
    ! [X0,X1] : hAPP_int_int(div_mod_int(number_number_of_int(bit0(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_zmod__number__of__Bit0) ).

fof(f1192,axiom,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X1) )
     => ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
           => ! [X3,X4] :
                ( ( is_int(X4)
                  & is_int(X3) )
               => ( ( X1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4)
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4)) )
                 => hBOOL(hAPP_int_bool(X0,X4)) ) ) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
           => ! [X3,X4] :
                ( ( is_int(X4)
                  & is_int(X3) )
               => ( ( X1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4)
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) )
                 => hBOOL(hAPP_int_bool(X0,X4)) ) ) )
          & ( X2 = zero_zero_int
           => hBOOL(hAPP_int_bool(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_split__zmod) ).

fof(f1193,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_zmult2__lemma__aux3) ).

fof(f1194,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),hAPP_int_int(times_times_int(X1),X3))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_zmult2__lemma__aux4) ).

fof(f1195,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_zmult2__lemma__aux1) ).

fof(f1196,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),zero_zero_int)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_zmult2__lemma__aux2) ).

fof(f1197,axiom,
    ! [X0,X1,X2,X3] :
      ( ( is_int(X3)
        & is_int(X1) )
     => ( X0 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3)
       => ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),zero_zero_int))
                & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ) )
            & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
                & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ) ) )
         => ( X1 != zero_zero_int
           => hAPP_int_int(div_mod_int(X0),X1) = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_divmod__int__rel__mod__eq) ).

fof(f1198,axiom,
    ! [X0] :
      ( hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
    <=> hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_neq__one__mod__two) ).

fof(f1199,axiom,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
     => hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) = hAPP_int_int(minus_minus_int(X0),one_one_int) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_zmod__minus1) ).

fof(f1200,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_pos__zmod__mult__2) ).

fof(f1201,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int
       => ? [X2] :
            ( X0 = hAPP_int_int(times_times_int(X1),X2)
            & is_int(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_zmod__eq__0D) ).

fof(f1202,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
     => hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(X2,X0)),standardRes(X2,X1)),hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_StandardRes__prop4) ).

fof(f1203,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_mod__le__divisor) ).

fof(f1204,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_mod__less__divisor) ).

fof(f1205,axiom,
    ! [X0,X1] :
      ( hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat
    <=> ? [X2] : X0 = hAPP_nat_nat(times_times_nat(X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_mod__eq__0__iff) ).

fof(f1207,axiom,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
       => hAPP_nat_nat(div_mod_nat(X0),X1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X1) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
       => hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_mod__if) ).

fof(f1208,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),X1) = hAPP_nat_nat(div_mod_nat(X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_mod__mult__self3) ).

fof(f1209,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => hAPP_nat_nat(div_mod_nat(X1),X0) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_le__mod__geq) ).

fof(f1210,axiom,
    ! [X0,X1] : standardRes(X0,X1) = hAPP_int_int(div_mod_int(X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_StandardRes__def) ).

fof(f1211,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X2) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_mod__mult__distrib) ).

fof(f1212,axiom,
    ! [X0,X1,X2] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(div_mod_nat(X1),X2)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_mod__mult__distrib2) ).

fof(f1213,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_mod__less) ).

fof(f1214,axiom,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_mod__less__eq__dividend) ).

fof(f1216,axiom,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
    <=> standardRes(X1,X0) != zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_StandardRes__prop3) ).

fof(f1217,axiom,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,standardRes(X1,X0)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_StandardRes__prop1) ).

fof(f1218,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(X1,X0)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_StandardRes__ubound) ).

fof(f1219,axiom,
    ! [X0,X1] :
      ( is_int(X0)
     => ( hBOOL(member_int(X0,sr(X1)))
       => standardRes(X1,X0) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1193_StandardRes__SR__prop) ).

fof(f1220,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
    <=> ( ( X2 != zero_zero_nat
         => ! [X3,X4] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
             => ( X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4)
               => hBOOL(hAPP_nat_bool(X0,X4)) ) ) )
        & ( X2 = zero_zero_nat
         => hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_split__mod) ).

fof(f1221,axiom,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X3))),X1)),hAPP_nat_nat(times_times_nat(X2),X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_mod__lemma) ).

fof(f1222,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(X1,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_StandardRes__lbound) ).

fof(f1223,axiom,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( standardRes(X2,X0) = standardRes(X2,X1)
      <=> hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_StandardRes__prop2) ).

fof(f1224,axiom,
    ! [X0,X1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

fof(f1225,axiom,
    ! [X0,X1] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

fof(f1226,axiom,
    ! [X0,X1] :
      ( hBOOL(X1)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

fof(f1227,axiom,
    ! [X0,X1,X2] : hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).

fof(f1228,axiom,
    ! [X0,X1,X2] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(f1229,axiom,
    ! [X0,X1,X2] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

fof(f1230,conjecture,
    ? [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1231,negated_conjecture,
    ~ ? [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
    inference(negated_conjecture,[status(cth)],[f1230]) ).

fof(f1232,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( ! [X3] :
            ( is_int(X3)
           => ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),X2))) ) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ! [X4] :
              ( hBOOL(hAPP_int_bool(X1,X4))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ) ) ),
    inference(rectify,[],[f1091]) ).

fof(f1233,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
     => ( ! [X3] :
            ( is_int(X3)
           => ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),X2))) ) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
         => ! [X4] :
              ( hBOOL(hAPP_int_bool(X1,X4))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ) ) ),
    inference(rectify,[],[f1092]) ).

fof(f1234,plain,
    ! [X0,X1,X2] :
      ( ( is_int(X2)
        & is_int(X1) )
     => ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      <=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
           => ! [X5,X6] :
                ( ( is_int(X6)
                  & is_int(X5) )
               => ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) = X1
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6)) )
                 => hBOOL(hAPP_int_bool(X0,X6)) ) ) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
           => ! [X3,X4] :
                ( ( is_int(X4)
                  & is_int(X3) )
               => ( ( X1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4)
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
                    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) )
                 => hBOOL(hAPP_int_bool(X0,X4)) ) ) )
          & ( X2 = zero_zero_int
           => hBOOL(hAPP_int_bool(X0,X1)) ) ) ) ),
    inference(rectify,[],[f1192]) ).

fof(f1235,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(multInv(X0,X1)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f1236,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(multInv(X0,X1)) ),
    inference(flattening,[],[f1235]) ).

fof(f1237,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | is_int(zfact(X0)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f1240,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | is_int(number_number_of_int(X0)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f1241,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(legendre(X0,X1)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f1242,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(legendre(X0,X1)) ),
    inference(flattening,[],[f1241]) ).

fof(f1245,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(inv(X0,X1)) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f1246,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(inv(X0,X1)) ),
    inference(flattening,[],[f1245]) ).

fof(f1249,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | is_int(hAPP_int_int(X0,X1)) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f1251,plain,
    ( one_one_int != t
    | ? [X0,X1] :
        ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
        & is_int(X1)
        & is_int(X0) ) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f1252,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | ? [X0,X1] :
        ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
        & is_int(X1)
        & is_int(X0) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f1253,plain,
    ? [X0] :
      ( is_int(X0)
      & hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),X0) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f1258,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f1259,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ),
    inference(flattening,[],[f1258]) ).

fof(f1260,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f66]) ).

fof(f1261,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | X0 = X1 ),
    inference(flattening,[],[f1260]) ).

fof(f1263,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X3),X1))) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f1264,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X3),X1))) ),
    inference(flattening,[],[f1263]) ).

fof(f1265,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X0)),hAPP_int_int(plus_plus_int(X2),X0))) ),
    inference(ennf_transformation,[],[f101]) ).

fof(f1266,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2))) ),
    inference(ennf_transformation,[],[f102]) ).

fof(f1267,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
        | ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
            | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
            | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(X1) ) ) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
        | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(X0) ) ),
    inference(ennf_transformation,[],[f103]) ).

fof(f1269,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X1),X0))) ),
    inference(ennf_transformation,[],[f116]) ).

fof(f1270,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X1),X0))) ),
    inference(flattening,[],[f1269]) ).

fof(f1271,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) = number_number_of_int(X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f161]) ).

fof(f1272,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) = number_number_of_int(X1)
      <=> X0 = X1 ) ),
    inference(flattening,[],[f1271]) ).

fof(f1273,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( number267125858f_real(X0) = number267125858f_real(X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f162]) ).

fof(f1274,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( number267125858f_real(X0) = number267125858f_real(X1)
      <=> X0 = X1 ) ),
    inference(flattening,[],[f1273]) ).

fof(f1276,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( bit1(X0) = bit1(X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f166]) ).

fof(f1277,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( bit1(X0) = bit1(X1)
      <=> X0 = X1 ) ),
    inference(flattening,[],[f1276]) ).

fof(f1278,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( bit0(X0) = bit0(X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f167]) ).

fof(f1279,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( bit0(X0) = bit0(X1)
      <=> X0 = X1 ) ),
    inference(flattening,[],[f1278]) ).

fof(f1280,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | number_number_of_int(X0) = X0 ),
    inference(ennf_transformation,[],[f170]) ).

fof(f1285,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( X0 != X1
          & X2 != X3 )
      <=> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) ) ),
    inference(ennf_transformation,[],[f205]) ).

fof(f1286,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( X0 != X1
          & X2 != X3 )
      <=> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) ) ),
    inference(flattening,[],[f1285]) ).

fof(f1293,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(X0),one_one_int) = X0 ),
    inference(ennf_transformation,[],[f233]) ).

fof(f1294,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(one_one_int),X0) = X0 ),
    inference(ennf_transformation,[],[f234]) ).

fof(f1297,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) ),
    inference(ennf_transformation,[],[f240]) ).

fof(f1298,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) ),
    inference(flattening,[],[f1297]) ).

fof(f1303,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) ),
    inference(ennf_transformation,[],[f243]) ).

fof(f1304,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) ),
    inference(flattening,[],[f1303]) ).

fof(f1311,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | number_number_of_int(bit0(bit1(pls))) = X0
      | number_number_of_int(bit1(bit1(pls))) = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X0)) ),
    inference(ennf_transformation,[],[f316]) ).

fof(f1312,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | number_number_of_int(bit0(bit1(pls))) = X0
      | number_number_of_int(bit1(bit1(pls))) = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X0)) ),
    inference(flattening,[],[f1311]) ).

fof(f1313,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    inference(ennf_transformation,[],[f320]) ).

fof(f1314,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    inference(ennf_transformation,[],[f321]) ).

fof(f1315,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    inference(ennf_transformation,[],[f322]) ).

fof(f1316,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    inference(ennf_transformation,[],[f323]) ).

fof(f1317,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    inference(ennf_transformation,[],[f324]) ).

fof(f1318,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    inference(ennf_transformation,[],[f325]) ).

fof(f1325,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f329]) ).

fof(f1326,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f330]) ).

fof(f1327,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f331]) ).

fof(f1328,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ is_int(X1)
          | ~ hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          | X1 = X0 )
      & hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      & is_int(X0) ),
    inference(ennf_transformation,[],[f334]) ).

fof(f1329,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ is_int(X1)
          | ~ hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          | X1 = X0 )
      & hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      & is_int(X0) ),
    inference(flattening,[],[f1328]) ).

fof(f1330,plain,
    ? [X0] :
      ( is_int(X0)
      & hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f335]) ).

fof(f1331,plain,
    ? [X0] :
      ( is_int(X0)
      & hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(flattening,[],[f1330]) ).

fof(f1333,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(ennf_transformation,[],[f340]) ).

fof(f1334,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(ennf_transformation,[],[f341]) ).

fof(f1335,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f342]) ).

fof(f1336,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X3),X1))) ),
    inference(ennf_transformation,[],[f343]) ).

fof(f1337,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X3),X1))) ),
    inference(flattening,[],[f1336]) ).

fof(f1338,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X3),X1))) ),
    inference(ennf_transformation,[],[f344]) ).

fof(f1339,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X3),X1))) ),
    inference(flattening,[],[f1338]) ).

fof(f1340,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X3),X1))) ),
    inference(ennf_transformation,[],[f345]) ).

fof(f1341,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X3),X1))) ),
    inference(flattening,[],[f1340]) ).

fof(f1342,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),X3)) ),
    inference(ennf_transformation,[],[f346]) ).

fof(f1343,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),X3)) ),
    inference(flattening,[],[f1342]) ).

fof(f1344,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),X3)) ),
    inference(ennf_transformation,[],[f347]) ).

fof(f1345,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),X3)) ),
    inference(flattening,[],[f1344]) ).

fof(f1346,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),X3)) ),
    inference(ennf_transformation,[],[f348]) ).

fof(f1347,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),X3)) ),
    inference(flattening,[],[f1346]) ).

fof(f1348,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X2),X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(ennf_transformation,[],[f349]) ).

fof(f1349,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X2),X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(flattening,[],[f1348]) ).

fof(f1350,plain,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(ennf_transformation,[],[f350]) ).

fof(f1351,plain,
    ! [X0,X1,X2] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(flattening,[],[f1350]) ).

fof(f1352,plain,
    ! [X0,X1,X2] :
      ( hAPP_nat_real(power_power_real(X0),X1) != hAPP_nat_real(power_power_real(X2),X1)
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(ennf_transformation,[],[f351]) ).

fof(f1353,plain,
    ! [X0,X1,X2] :
      ( hAPP_nat_real(power_power_real(X0),X1) != hAPP_nat_real(power_power_real(X2),X1)
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(flattening,[],[f1352]) ).

fof(f1354,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(ennf_transformation,[],[f352]) ).

fof(f1355,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(flattening,[],[f1354]) ).

fof(f1356,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | X1 = X0 ),
    inference(ennf_transformation,[],[f353]) ).

fof(f1357,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | X1 = X0 ),
    inference(flattening,[],[f1356]) ).

fof(f1360,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(ennf_transformation,[],[f355]) ).

fof(f1361,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(ennf_transformation,[],[f356]) ).

fof(f1363,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | zero_zero_int = X1
      | hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ),
    inference(ennf_transformation,[],[f358]) ).

fof(f1364,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | zero_zero_int = X1
      | hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ),
    inference(flattening,[],[f1363]) ).

fof(f1365,plain,
    ! [X0,X1] :
      ( zero_zero_real = X1
      | hAPP_nat_real(power_power_real(X1),X0) != zero_zero_real ),
    inference(ennf_transformation,[],[f359]) ).

fof(f1366,plain,
    ! [X0] :
      ( ( zero_zero_nat = X0
        | hAPP_nat_int(power_power_int(zero_zero_int),X0) = zero_zero_int )
      & ( zero_zero_nat != X0
        | hAPP_nat_int(power_power_int(zero_zero_int),X0) = one_one_int ) ),
    inference(ennf_transformation,[],[f360]) ).

fof(f1368,plain,
    ! [X0] :
      ( ( zero_zero_nat = X0
        | hAPP_nat_real(power_power_real(zero_zero_real),X0) = zero_zero_real )
      & ( zero_zero_nat != X0
        | hAPP_nat_real(power_power_real(zero_zero_real),X0) = one_one_real ) ),
    inference(ennf_transformation,[],[f362]) ).

fof(f1371,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(ennf_transformation,[],[f364]) ).

fof(f1372,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(flattening,[],[f1371]) ).

fof(f1373,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f365]) ).

fof(f1374,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(flattening,[],[f1373]) ).

fof(f1375,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(ennf_transformation,[],[f366]) ).

fof(f1376,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(flattening,[],[f1375]) ).

fof(f1379,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( X0 = hAPP_int_int(plus_plus_int(X0),X1)
      <=> X1 = zero_zero_int ) ),
    inference(ennf_transformation,[],[f379]) ).

fof(f1380,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( X0 = hAPP_int_int(plus_plus_int(X0),X1)
      <=> X1 = zero_zero_int ) ),
    inference(flattening,[],[f1379]) ).

fof(f1381,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(X0),X0) = zero_zero_int
      <=> X0 = zero_zero_int ) ),
    inference(ennf_transformation,[],[f382]) ).

fof(f1382,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
    inference(ennf_transformation,[],[f386]) ).

fof(f1383,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),zero_zero_int) = X0 ),
    inference(ennf_transformation,[],[f387]) ).

fof(f1386,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(ennf_transformation,[],[f390]) ).

fof(f1387,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(ennf_transformation,[],[f391]) ).

fof(f1388,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(flattening,[],[f1387]) ).

fof(f1389,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f392]) ).

fof(f1390,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(flattening,[],[f1389]) ).

fof(f1391,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(ennf_transformation,[],[f393]) ).

fof(f1392,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(flattening,[],[f1391]) ).

fof(f1393,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(ennf_transformation,[],[f394]) ).

fof(f1395,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(ennf_transformation,[],[f396]) ).

fof(f1396,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X2),one_one_int),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),X0)),one_one_int),X3)) ),
    inference(ennf_transformation,[],[f397]) ).

fof(f1397,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X4))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2))) ) ),
    inference(ennf_transformation,[],[f399]) ).

fof(f1398,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(ennf_transformation,[],[f400]) ).

fof(f1399,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(flattening,[],[f1398]) ).

fof(f1400,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(ennf_transformation,[],[f401]) ).

fof(f1401,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(flattening,[],[f1400]) ).

fof(f1402,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ),
    inference(ennf_transformation,[],[f402]) ).

fof(f1403,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ),
    inference(flattening,[],[f1402]) ).

fof(f1404,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(ennf_transformation,[],[f403]) ).

fof(f1405,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(flattening,[],[f1404]) ).

fof(f1406,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(ennf_transformation,[],[f404]) ).

fof(f1407,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(flattening,[],[f1406]) ).

fof(f1408,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(ennf_transformation,[],[f405]) ).

fof(f1409,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(flattening,[],[f1408]) ).

fof(f1410,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(ennf_transformation,[],[f406]) ).

fof(f1411,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(flattening,[],[f1410]) ).

fof(f1412,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(ennf_transformation,[],[f407]) ).

fof(f1413,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(flattening,[],[f1412]) ).

fof(f1414,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(ennf_transformation,[],[f408]) ).

fof(f1415,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(flattening,[],[f1414]) ).

fof(f1416,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f411]) ).

fof(f1417,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(flattening,[],[f1416]) ).

fof(f1418,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ is_int(X4)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X4
      | X0 = X1
      | X2 != X3
      | hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(X4),X0)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) ),
    inference(ennf_transformation,[],[f413]) ).

fof(f1419,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ is_int(X4)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X4
      | X0 = X1
      | X2 != X3
      | hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(X4),X0)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) ),
    inference(flattening,[],[f1418]) ).

fof(f1420,plain,
    ! [X0,X1,X2,X3,X4] :
      ( zero_zero_nat = X4
      | X0 = X1
      | X2 != X3
      | hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X4),X0)) != hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X1)) ),
    inference(ennf_transformation,[],[f414]) ).

fof(f1421,plain,
    ! [X0,X1,X2,X3,X4] :
      ( zero_zero_nat = X4
      | X0 = X1
      | X2 != X3
      | hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X4),X0)) != hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X1)) ),
    inference(flattening,[],[f1420]) ).

fof(f1422,plain,
    ! [X0,X1,X2,X3,X4] :
      ( zero_zero_real = X4
      | X0 = X1
      | X2 != X3
      | hAPP_real_real(plus_plus_real(X2),hAPP_real_real(times_times_real(X4),X0)) != hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X1)) ),
    inference(ennf_transformation,[],[f415]) ).

fof(f1423,plain,
    ! [X0,X1,X2,X3,X4] :
      ( zero_zero_real = X4
      | X0 = X1
      | X2 != X3
      | hAPP_real_real(plus_plus_real(X2),hAPP_real_real(times_times_real(X4),X0)) != hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X1)) ),
    inference(flattening,[],[f1422]) ).

fof(f1424,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_nat_int(power_power_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(ennf_transformation,[],[f416]) ).

fof(f1425,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_nat_int(power_power_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(flattening,[],[f1424]) ).

fof(f1426,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f429]) ).

fof(f1427,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(flattening,[],[f1426]) ).

fof(f1432,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0))),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(ennf_transformation,[],[f433]) ).

fof(f1433,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0))),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(flattening,[],[f1432]) ).

fof(f1434,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0))),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(ennf_transformation,[],[f434]) ).

fof(f1435,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0))),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(flattening,[],[f1434]) ).

fof(f1436,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(ennf_transformation,[],[f435]) ).

fof(f1437,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(flattening,[],[f1436]) ).

fof(f1438,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X1),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(ennf_transformation,[],[f436]) ).

fof(f1439,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X1),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(flattening,[],[f1438]) ).

fof(f1440,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f439]) ).

fof(f1441,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(flattening,[],[f1440]) ).

fof(f1442,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ) ),
    inference(ennf_transformation,[],[f441]) ).

fof(f1443,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f444]) ).

fof(f1444,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    inference(flattening,[],[f1443]) ).

fof(f1445,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
    inference(ennf_transformation,[],[f446]) ).

fof(f1446,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
    inference(ennf_transformation,[],[f449]) ).

fof(f1447,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ( hAPP_int_int(times_times_int(X1),X0) = one_one_int
      <=> ( X0 = one_one_int
          & X1 = one_one_int ) ) ),
    inference(ennf_transformation,[],[f453]) ).

fof(f1448,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ( hAPP_int_int(times_times_int(X1),X0) = one_one_int
      <=> ( X0 = one_one_int
          & X1 = one_one_int ) ) ),
    inference(flattening,[],[f1447]) ).

fof(f1449,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X0))) ),
    inference(ennf_transformation,[],[f463]) ).

fof(f1451,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(ennf_transformation,[],[f471]) ).

fof(f1452,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(flattening,[],[f1451]) ).

fof(f1453,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f472]) ).

fof(f1454,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(flattening,[],[f1453]) ).

fof(f1455,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(ennf_transformation,[],[f473]) ).

fof(f1456,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(flattening,[],[f1455]) ).

fof(f1457,plain,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f474]) ).

fof(f1458,plain,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | X0 = X1 ),
    inference(flattening,[],[f1457]) ).

fof(f1459,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f475]) ).

fof(f1460,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | X0 = X1 ),
    inference(flattening,[],[f1459]) ).

fof(f1461,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f476]) ).

fof(f1462,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | X0 = X1 ),
    inference(flattening,[],[f1461]) ).

fof(f1463,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))))
      <=> X0 != zero_zero_int ) ),
    inference(ennf_transformation,[],[f480]) ).

fof(f1464,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f482]) ).

fof(f1465,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(flattening,[],[f1464]) ).

fof(f1472,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f504]) ).

fof(f1473,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
      <=> ( X1 = zero_zero_int
          & X0 = zero_zero_int ) ) ),
    inference(flattening,[],[f1472]) ).

fof(f1474,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f508]) ).

fof(f1475,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
      <=> ( X1 != zero_zero_int
          | X0 != zero_zero_int ) ) ),
    inference(flattening,[],[f1474]) ).

fof(f1476,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(ennf_transformation,[],[f511]) ).

fof(f1477,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(ennf_transformation,[],[f512]) ).

fof(f1478,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(ennf_transformation,[],[f513]) ).

fof(f1479,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(ennf_transformation,[],[f514]) ).

fof(f1480,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(flattening,[],[f1479]) ).

fof(f1481,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f515]) ).

fof(f1482,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(flattening,[],[f1481]) ).

fof(f1483,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(ennf_transformation,[],[f516]) ).

fof(f1484,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(flattening,[],[f1483]) ).

fof(f1485,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ( hAPP_nat_real(power_power_real(X2),X0) = hAPP_nat_real(power_power_real(X2),X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f517]) ).

fof(f1486,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ( hAPP_nat_nat(power_power_nat(X2),X0) = hAPP_nat_nat(power_power_nat(X2),X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f518]) ).

fof(f1487,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ( hAPP_nat_int(power_power_int(X2),X0) = hAPP_nat_int(power_power_int(X2),X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f519]) ).

fof(f1491,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f523]) ).

fof(f1492,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1491]) ).

fof(f1493,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f524]) ).

fof(f1494,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1493]) ).

fof(f1495,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f525]) ).

fof(f1496,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1495]) ).

fof(f1497,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(ennf_transformation,[],[f526]) ).

fof(f1498,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(flattening,[],[f1497]) ).

fof(f1499,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f527]) ).

fof(f1500,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(flattening,[],[f1499]) ).

fof(f1501,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(ennf_transformation,[],[f528]) ).

fof(f1502,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(flattening,[],[f1501]) ).

fof(f1503,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(ennf_transformation,[],[f530]) ).

fof(f1504,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(flattening,[],[f1503]) ).

fof(f1505,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(bit0(bit1(pls)))))
      | X0 = one_one_int
      | X0 = zero_zero_int ),
    inference(ennf_transformation,[],[f531]) ).

fof(f1506,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(bit0(bit1(pls)))))
      | X0 = one_one_int
      | X0 = zero_zero_int ),
    inference(flattening,[],[f1505]) ).

fof(f1507,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_real))
      | X0 = zero_zero_real ),
    inference(ennf_transformation,[],[f532]) ).

fof(f1508,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_int))
      | X0 = zero_zero_int ),
    inference(ennf_transformation,[],[f533]) ).

fof(f1509,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_int))
      | X0 = zero_zero_int ),
    inference(flattening,[],[f1508]) ).

fof(f1510,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(zprime,X0))
      <=> ( ! [X1] :
              ( ~ is_int(X1)
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
              | X1 = X0
              | X1 = one_one_int )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ) ),
    inference(ennf_transformation,[],[f534]) ).

fof(f1511,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(zprime,X0))
      <=> ( ! [X1] :
              ( ~ is_int(X1)
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
              | X1 = X0
              | X1 = one_one_int )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ) ),
    inference(flattening,[],[f1510]) ).

fof(f1512,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int)) ),
    inference(ennf_transformation,[],[f535]) ).

fof(f1513,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int)) ),
    inference(flattening,[],[f1512]) ).

fof(f1514,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
    inference(ennf_transformation,[],[f536]) ).

fof(f1515,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
    inference(flattening,[],[f1514]) ).

fof(f1516,plain,
    ? [X0] :
      ( is_int(X0)
      & hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))) ),
    inference(ennf_transformation,[],[f538]) ).

fof(f1517,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f543]) ).

fof(f1518,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1517]) ).

fof(f1519,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( bit1(X0) = min
      <=> X0 = min ) ),
    inference(ennf_transformation,[],[f544]) ).

fof(f1521,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f566]) ).

fof(f1522,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(flattening,[],[f1521]) ).

fof(f1523,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | X0 = number_number_of_int(min)
      | X0 = one_one_int ),
    inference(ennf_transformation,[],[f577]) ).

fof(f1524,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | X0 = number_number_of_int(min)
      | X0 = one_one_int ),
    inference(flattening,[],[f1523]) ).

fof(f1525,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) = one_one_int
      <=> ( ( X1 = number_number_of_int(min)
            & X0 = number_number_of_int(min) )
          | ( X1 = one_one_int
            & X0 = one_one_int ) ) ) ),
    inference(ennf_transformation,[],[f578]) ).

fof(f1526,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) = one_one_int
      <=> ( ( X1 = number_number_of_int(min)
            & X0 = number_number_of_int(min) )
          | ( X1 = one_one_int
            & X0 = one_one_int ) ) ) ),
    inference(flattening,[],[f1525]) ).

fof(f1527,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(ennf_transformation,[],[f579]) ).

fof(f1528,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(flattening,[],[f1527]) ).

fof(f1529,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(ennf_transformation,[],[f580]) ).

fof(f1530,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(flattening,[],[f1529]) ).

fof(f1531,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(ennf_transformation,[],[f581]) ).

fof(f1532,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(flattening,[],[f1531]) ).

fof(f1533,plain,
    ! [X0,X1] :
      ( ( one_one_real != X0
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(ennf_transformation,[],[f582]) ).

fof(f1534,plain,
    ! [X0,X1] :
      ( ( one_one_nat != X0
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(ennf_transformation,[],[f583]) ).

fof(f1535,plain,
    ! [X0,X1] :
      ( ( one_one_int != X0
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(ennf_transformation,[],[f584]) ).

fof(f1538,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
        | hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(X2),X0))),X1) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
        | hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) = zero_zero_nat ) ),
    inference(ennf_transformation,[],[f592]) ).

fof(f1539,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
        | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
        | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = zero_zero_nat ) ),
    inference(ennf_transformation,[],[f593]) ).

fof(f1548,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f599]) ).

fof(f1549,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
      <=> X0 = X1 ) ),
    inference(flattening,[],[f1548]) ).

fof(f1550,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),X0),hAPP_int_int(times_times_int(X3),X1)),X4)) ),
    inference(ennf_transformation,[],[f601]) ).

fof(f1551,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),X0),hAPP_int_int(times_times_int(X3),X1)),X4)) ),
    inference(flattening,[],[f1550]) ).

fof(f1552,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X0),X2)),X3)) ),
    inference(ennf_transformation,[],[f602]) ).

fof(f1553,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),hAPP_int_int(times_times_int(X2),X0)),X3)) ),
    inference(ennf_transformation,[],[f603]) ).

fof(f1554,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X2),X0),hAPP_int_int(plus_plus_int(X3),X1)),X4)) ),
    inference(ennf_transformation,[],[f605]) ).

fof(f1555,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X2),X0),hAPP_int_int(plus_plus_int(X3),X1)),X4)) ),
    inference(flattening,[],[f1554]) ).

fof(f1556,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1)) = zero_zero_int
      <=> ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f610]) ).

fof(f1559,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X0))) ),
    inference(ennf_transformation,[],[f613]) ).

fof(f1560,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X0))) ),
    inference(flattening,[],[f1559]) ).

fof(f1561,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1)) ),
    inference(ennf_transformation,[],[f614]) ).

fof(f1562,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1)) ),
    inference(flattening,[],[f1561]) ).

fof(f1563,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(ennf_transformation,[],[f615]) ).

fof(f1564,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X1)
      | ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      <=> ? [X3] :
            ( X1 = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3))
            & is_int(X3) ) ) ),
    inference(ennf_transformation,[],[f616]) ).

fof(f1565,plain,
    ! [X0] :
      ( ( number_number_of_nat(X0) = zero_zero_nat
        | hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real )
      & ( number_number_of_nat(X0) != zero_zero_nat
        | hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real ) ),
    inference(ennf_transformation,[],[f617]) ).

fof(f1566,plain,
    ! [X0] :
      ( ( number_number_of_nat(X0) = zero_zero_nat
        | hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat )
      & ( number_number_of_nat(X0) != zero_zero_nat
        | hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat ) ),
    inference(ennf_transformation,[],[f618]) ).

fof(f1567,plain,
    ! [X0] :
      ( ( number_number_of_nat(X0) = zero_zero_nat
        | hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) = zero_zero_int )
      & ( number_number_of_nat(X0) != zero_zero_nat
        | hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) = one_one_int ) ),
    inference(ennf_transformation,[],[f619]) ).

fof(f1568,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1))
      | X2 = X0 ),
    inference(ennf_transformation,[],[f620]) ).

fof(f1569,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1))
      | X2 = X0 ),
    inference(flattening,[],[f1568]) ).

fof(f1572,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
    inference(ennf_transformation,[],[f623]) ).

fof(f1573,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
    inference(flattening,[],[f1572]) ).

fof(f1574,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ),
    inference(ennf_transformation,[],[f624]) ).

fof(f1575,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ),
    inference(flattening,[],[f1574]) ).

fof(f1576,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4)) ),
    inference(ennf_transformation,[],[f625]) ).

fof(f1577,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4)) ),
    inference(flattening,[],[f1576]) ).

fof(f1578,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
    inference(ennf_transformation,[],[f626]) ).

fof(f1579,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
    inference(flattening,[],[f1578]) ).

fof(f1580,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(ennf_transformation,[],[f627]) ).

fof(f1581,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(flattening,[],[f1580]) ).

fof(f1582,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f628]) ).

fof(f1583,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(flattening,[],[f1582]) ).

fof(f1586,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2))
      | hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) ),
    inference(ennf_transformation,[],[f632]) ).

fof(f1587,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2))
      | hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) ),
    inference(flattening,[],[f1586]) ).

fof(f1588,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,number_number_of_int(min)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(ennf_transformation,[],[f633]) ).

fof(f1589,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,number_number_of_int(min)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(flattening,[],[f1588]) ).

fof(f1590,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0)) ),
    inference(ennf_transformation,[],[f634]) ).

fof(f1591,plain,
    ( hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),number_number_of_int(min)))
    | legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)) != one_one_int ),
    inference(ennf_transformation,[],[f636]) ).

fof(f1592,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X0)
      | hAPP_int_int(minus_minus_int(X0),X1) != X2
      | X0 = hAPP_int_int(plus_plus_int(X2),X1) ),
    inference(ennf_transformation,[],[f637]) ).

fof(f1593,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X0)
      | hAPP_int_int(minus_minus_int(X0),X1) != X2
      | X0 = hAPP_int_int(plus_plus_int(X2),X1) ),
    inference(flattening,[],[f1592]) ).

fof(f1594,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(minus_minus_int(X0),pls) = X0 ),
    inference(ennf_transformation,[],[f640]) ).

fof(f1595,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X2),X0),hAPP_int_int(minus_minus_int(X3),X1)),X4)) ),
    inference(ennf_transformation,[],[f644]) ).

fof(f1596,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X2),X0),hAPP_int_int(minus_minus_int(X3),X1)),X4)) ),
    inference(flattening,[],[f1595]) ).

fof(f1597,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(ennf_transformation,[],[f645]) ).

fof(f1598,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(flattening,[],[f1597]) ).

fof(f1599,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(ennf_transformation,[],[f658]) ).

fof(f1600,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(flattening,[],[f1599]) ).

fof(f1601,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | X1 != X3
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X4))
      | hBOOL(hAPP_int_bool(zcong(X2,X0),X4)) ),
    inference(ennf_transformation,[],[f664]) ).

fof(f1602,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | X1 != X3
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X4))
      | hBOOL(hAPP_int_bool(zcong(X2,X0),X4)) ),
    inference(flattening,[],[f1601]) ).

fof(f1603,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(ennf_transformation,[],[f666]) ).

fof(f1604,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(flattening,[],[f1603]) ).

fof(f1605,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | X0 = hAPP_int_int(minus_minus_int(X1),one_one_int)
      | X0 = one_one_int ),
    inference(ennf_transformation,[],[f667]) ).

fof(f1606,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | X0 = hAPP_int_int(minus_minus_int(X1),one_one_int)
      | X0 = one_one_int ),
    inference(flattening,[],[f1605]) ).

fof(f1607,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4))
      <=> hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4)) ) ),
    inference(ennf_transformation,[],[f670]) ).

fof(f1608,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4))
      <=> hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4)) ) ),
    inference(ennf_transformation,[],[f671]) ).

fof(f1609,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X1),X0),hAPP_int_int(plus_plus_int(X2),X0)),X3)) ),
    inference(ennf_transformation,[],[f672]) ).

fof(f1610,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X0),hAPP_nat_int(power_power_int(X2),X0)),X3)) ),
    inference(ennf_transformation,[],[f673]) ).

fof(f1611,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | X2 = X1 ),
    inference(ennf_transformation,[],[f678]) ).

fof(f1612,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | X2 = X1 ),
    inference(flattening,[],[f1611]) ).

fof(f1613,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f679]) ).

fof(f1614,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0)) ),
    inference(flattening,[],[f1613]) ).

fof(f1615,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(ennf_transformation,[],[f680]) ).

fof(f1616,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(flattening,[],[f1615]) ).

fof(f1617,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(ennf_transformation,[],[f683]) ).

fof(f1618,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(flattening,[],[f1617]) ).

fof(f1619,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0))
      | X1 = zero_zero_int ),
    inference(ennf_transformation,[],[f684]) ).

fof(f1620,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0))
      | X1 = zero_zero_int ),
    inference(flattening,[],[f1619]) ).

fof(f1621,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2))) ),
    inference(ennf_transformation,[],[f685]) ).

fof(f1622,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2))) ),
    inference(flattening,[],[f1621]) ).

fof(f1623,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),zero_zero_int),X2)) ),
    inference(ennf_transformation,[],[f687]) ).

fof(f1624,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),zero_zero_int),X2)) ),
    inference(flattening,[],[f1623]) ).

fof(f1631,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)))
      | legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)) = one_one_int ),
    inference(ennf_transformation,[],[f691]) ).

fof(f1632,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
        | ( ( hBOOL(hAPP_int_bool(quadRes(X1),X0))
            | legendre(X0,X1) = number_number_of_int(min) )
          & ( ~ hBOOL(hAPP_int_bool(quadRes(X1),X0))
            | legendre(X0,X1) = one_one_int ) ) )
      & ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
        | legendre(X0,X1) = zero_zero_int ) ),
    inference(ennf_transformation,[],[f692]) ).

fof(f1633,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1))
      | X1 = X0
      | X1 = zero_zero_nat ),
    inference(ennf_transformation,[],[f693]) ).

fof(f1634,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1))
      | X1 = X0
      | X1 = zero_zero_nat ),
    inference(flattening,[],[f1633]) ).

fof(f1635,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | one_one_real != hAPP_real_real(plus_plus_real(X1),X0)
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X3)),hAPP_real_real(times_times_real(X0),X2))),X4)) ),
    inference(ennf_transformation,[],[f696]) ).

fof(f1636,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | one_one_real != hAPP_real_real(plus_plus_real(X1),X0)
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X3)),hAPP_real_real(times_times_real(X0),X2))),X4)) ),
    inference(flattening,[],[f1635]) ).

fof(f1637,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | one_one_int != hAPP_int_int(plus_plus_int(X1),X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(times_times_int(X0),X2))),X4)) ),
    inference(ennf_transformation,[],[f697]) ).

fof(f1638,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | one_one_int != hAPP_int_int(plus_plus_int(X1),X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(times_times_int(X0),X2))),X4)) ),
    inference(flattening,[],[f1637]) ).

fof(f1639,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ),
    inference(ennf_transformation,[],[f702]) ).

fof(f1640,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ),
    inference(flattening,[],[f1639]) ).

fof(f1643,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0)) ),
    inference(ennf_transformation,[],[f707]) ).

fof(f1644,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0)) ),
    inference(flattening,[],[f1643]) ).

fof(f1647,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    inference(ennf_transformation,[],[f709]) ).

fof(f1648,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    inference(flattening,[],[f1647]) ).

fof(f1649,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X0),X2))) ),
    inference(ennf_transformation,[],[f717]) ).

fof(f1650,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_nat(power_power_nat(X0),X1) ),
    inference(ennf_transformation,[],[f718]) ).

fof(f1651,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_real(power_power_real(X0),X1) ),
    inference(ennf_transformation,[],[f719]) ).

fof(f1652,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) = hAPP_nat_int(power_power_int(X0),X1) ),
    inference(ennf_transformation,[],[f720]) ).

fof(f1653,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat = X1
        | hAPP_nat_nat(times_times_nat(X1),X0) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),one_one_nat)),X0)) )
      & ( zero_zero_nat != X1
        | hAPP_nat_nat(times_times_nat(X1),X0) = zero_zero_nat ) ),
    inference(ennf_transformation,[],[f721]) ).

fof(f1654,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat = X1
        | hAPP_nat_nat(power_power_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))) )
      & ( zero_zero_nat != X1
        | hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat ) ),
    inference(ennf_transformation,[],[f722]) ).

fof(f1667,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) = zero_zero_int
      <=> ( X1 = zero_zero_int
          | X0 = zero_zero_int ) ) ),
    inference(ennf_transformation,[],[f731]) ).

fof(f1668,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) = zero_zero_int
      <=> ( X1 = zero_zero_int
          | X0 = zero_zero_int ) ) ),
    inference(flattening,[],[f1667]) ).

fof(f1669,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0))
      | X0 = zero_zero_real ),
    inference(ennf_transformation,[],[f750]) ).

fof(f1671,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),X0))
      | X0 = zero_zero_int ),
    inference(ennf_transformation,[],[f752]) ).

fof(f1672,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),X0))
      | X0 = zero_zero_int ),
    inference(flattening,[],[f1671]) ).

fof(f1673,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2)) ),
    inference(ennf_transformation,[],[f755]) ).

fof(f1674,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f756]) ).

fof(f1675,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2)) ),
    inference(ennf_transformation,[],[f757]) ).

fof(f1676,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2)) ),
    inference(ennf_transformation,[],[f758]) ).

fof(f1677,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    inference(ennf_transformation,[],[f759]) ).

fof(f1678,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    inference(ennf_transformation,[],[f760]) ).

fof(f1682,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(ennf_transformation,[],[f764]) ).

fof(f1683,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(flattening,[],[f1682]) ).

fof(f1684,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(ennf_transformation,[],[f765]) ).

fof(f1685,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(flattening,[],[f1684]) ).

fof(f1686,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(ennf_transformation,[],[f766]) ).

fof(f1687,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(flattening,[],[f1686]) ).

fof(f1688,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(ennf_transformation,[],[f767]) ).

fof(f1689,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f768]) ).

fof(f1690,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(ennf_transformation,[],[f769]) ).

fof(f1691,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X2),X0))) ),
    inference(ennf_transformation,[],[f770]) ).

fof(f1692,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f771]) ).

fof(f1693,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(ennf_transformation,[],[f772]) ).

fof(f1694,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(plus_plus_real(X2),X0))) ),
    inference(ennf_transformation,[],[f779]) ).

fof(f1695,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(plus_plus_real(X2),X0))) ),
    inference(flattening,[],[f1694]) ).

fof(f1696,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f780]) ).

fof(f1697,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(flattening,[],[f1696]) ).

fof(f1698,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(plus_plus_int(X2),X0))) ),
    inference(ennf_transformation,[],[f781]) ).

fof(f1699,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(plus_plus_int(X2),X0))) ),
    inference(flattening,[],[f1698]) ).

fof(f1700,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(minus_minus_real(X2),X0))) ),
    inference(ennf_transformation,[],[f785]) ).

fof(f1701,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(minus_minus_real(X2),X0))) ),
    inference(flattening,[],[f1700]) ).

fof(f1702,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X2),X0))) ),
    inference(ennf_transformation,[],[f786]) ).

fof(f1703,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X2),X0))) ),
    inference(flattening,[],[f1702]) ).

fof(f1704,plain,
    ! [X0,X1,X2] :
      ( zero_zero_real = X2
      | ( hAPP_real_real(times_times_real(X0),X2) = hAPP_real_real(times_times_real(X1),X2)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f787]) ).

fof(f1705,plain,
    ! [X0,X1,X2] :
      ( zero_zero_real = X2
      | ( hAPP_real_real(times_times_real(X2),X0) = hAPP_real_real(times_times_real(X2),X1)
      <=> X0 = X1 ) ),
    inference(ennf_transformation,[],[f788]) ).

fof(f1706,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(ennf_transformation,[],[f789]) ).

fof(f1707,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(flattening,[],[f1706]) ).

fof(f1710,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f795]) ).

fof(f1712,plain,
    ! [X0,X1] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat)) ),
    inference(ennf_transformation,[],[f797]) ).

fof(f1713,plain,
    ! [X0,X1] :
      ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) )
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(ennf_transformation,[],[f798]) ).

fof(f1716,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(ennf_transformation,[],[f801]) ).

fof(f1717,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(flattening,[],[f1716]) ).

fof(f1720,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(ennf_transformation,[],[f803]) ).

fof(f1721,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(flattening,[],[f1720]) ).

fof(f1722,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(ennf_transformation,[],[f804]) ).

fof(f1723,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(flattening,[],[f1722]) ).

fof(f1726,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(ennf_transformation,[],[f806]) ).

fof(f1727,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(flattening,[],[f1726]) ).

fof(f1728,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(ennf_transformation,[],[f807]) ).

fof(f1729,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(flattening,[],[f1728]) ).

fof(f1730,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(ennf_transformation,[],[f808]) ).

fof(f1731,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(flattening,[],[f1730]) ).

fof(f1732,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(ennf_transformation,[],[f809]) ).

fof(f1733,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(flattening,[],[f1732]) ).

fof(f1734,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(ennf_transformation,[],[f810]) ).

fof(f1735,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(flattening,[],[f1734]) ).

fof(f1740,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(ennf_transformation,[],[f813]) ).

fof(f1741,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(flattening,[],[f1740]) ).

fof(f1742,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(ennf_transformation,[],[f814]) ).

fof(f1743,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(flattening,[],[f1742]) ).

fof(f1748,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X0)),hAPP_real_real(times_times_real(X2),X0))) ),
    inference(ennf_transformation,[],[f817]) ).

fof(f1749,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X0)),hAPP_real_real(times_times_real(X2),X0))) ),
    inference(flattening,[],[f1748]) ).

fof(f1752,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(ennf_transformation,[],[f819]) ).

fof(f1753,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(flattening,[],[f1752]) ).

fof(f1808,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(ennf_transformation,[],[f853]) ).

fof(f1809,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(flattening,[],[f1808]) ).

fof(f1810,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(ennf_transformation,[],[f854]) ).

fof(f1811,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(flattening,[],[f1810]) ).

fof(f1816,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(ennf_transformation,[],[f857]) ).

fof(f1817,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(flattening,[],[f1816]) ).

fof(f1818,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ) ),
    inference(ennf_transformation,[],[f858]) ).

fof(f1819,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ) ),
    inference(ennf_transformation,[],[f859]) ).

fof(f1820,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(ennf_transformation,[],[f860]) ).

fof(f1821,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(flattening,[],[f1820]) ).

fof(f1824,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f862]) ).

fof(f1825,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(flattening,[],[f1824]) ).

fof(f1826,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
    inference(ennf_transformation,[],[f863]) ).

fof(f1827,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
    inference(flattening,[],[f1826]) ).

fof(f1832,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(ennf_transformation,[],[f866]) ).

fof(f1833,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(flattening,[],[f1832]) ).

fof(f1838,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real)) ),
    inference(ennf_transformation,[],[f869]) ).

fof(f1839,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real)) ),
    inference(flattening,[],[f1838]) ).

fof(f1842,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(ennf_transformation,[],[f871]) ).

fof(f1843,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(flattening,[],[f1842]) ).

fof(f1848,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(ennf_transformation,[],[f874]) ).

fof(f1849,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(flattening,[],[f1848]) ).

fof(f1850,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    inference(ennf_transformation,[],[f875]) ).

fof(f1851,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(ennf_transformation,[],[f876]) ).

fof(f1854,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1))) ),
    inference(ennf_transformation,[],[f884]) ).

fof(f1855,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1))) ),
    inference(flattening,[],[f1854]) ).

fof(f1858,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    inference(ennf_transformation,[],[f887]) ).

fof(f1859,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    inference(ennf_transformation,[],[f888]) ).

fof(f1860,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      <=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    inference(ennf_transformation,[],[f889]) ).

fof(f1861,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(ennf_transformation,[],[f890]) ).

fof(f1862,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(flattening,[],[f1861]) ).

fof(f1863,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(ennf_transformation,[],[f891]) ).

fof(f1864,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(flattening,[],[f1863]) ).

fof(f1865,plain,
    ! [X0,X1,X2] :
      ( zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f893]) ).

fof(f1866,plain,
    ! [X0,X1,X2] :
      ( zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(flattening,[],[f1865]) ).

fof(f1869,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0)) ),
    inference(ennf_transformation,[],[f896]) ).

fof(f1870,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0)) ),
    inference(flattening,[],[f1869]) ).

fof(f1871,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ? [X2] :
          ( hAPP_nat_real(power_power_real(X2),X1) = X0
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ),
    inference(ennf_transformation,[],[f898]) ).

fof(f1872,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ? [X2] :
          ( hAPP_nat_real(power_power_real(X2),X1) = X0
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ),
    inference(flattening,[],[f1871]) ).

fof(f1873,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ? [X2] :
          ( ! [X3] :
              ( hAPP_nat_real(power_power_real(X3),X1) != X0
              | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
              | X3 = X2 )
          & hAPP_nat_real(power_power_real(X2),X1) = X0
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ),
    inference(ennf_transformation,[],[f899]) ).

fof(f1874,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ? [X2] :
          ( ! [X3] :
              ( hAPP_nat_real(power_power_real(X3),X1) != X0
              | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
              | X3 = X2 )
          & hAPP_nat_real(power_power_real(X2),X1) = X0
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ) ),
    inference(flattening,[],[f1873]) ).

fof(f1875,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1))
      <=> X0 = one_one_nat ) ),
    inference(ennf_transformation,[],[f900]) ).

fof(f1876,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X0)),X1))
      <=> X0 = one_one_nat ) ),
    inference(ennf_transformation,[],[f901]) ).

fof(f1877,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0)) ),
    inference(ennf_transformation,[],[f908]) ).

fof(f1878,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0)) ),
    inference(flattening,[],[f1877]) ).

fof(f1879,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f909]) ).

fof(f1880,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | X0 = X1 ),
    inference(flattening,[],[f1879]) ).

fof(f1881,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X0),X1)
      | zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X1),X0)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f913]) ).

fof(f1882,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X0),X1)
      | zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X1),X0)
      | X0 = X1 ),
    inference(flattening,[],[f1881]) ).

fof(f1889,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(ennf_transformation,[],[f921]) ).

fof(f1890,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(flattening,[],[f1889]) ).

fof(f1891,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)) ),
    inference(ennf_transformation,[],[f922]) ).

fof(f1920,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(ennf_transformation,[],[f937]) ).

fof(f1921,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(flattening,[],[f1920]) ).

fof(f1939,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f952]) ).

fof(f1940,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(flattening,[],[f1939]) ).

fof(f1942,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ),
    inference(ennf_transformation,[],[f966]) ).

fof(f1943,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ),
    inference(flattening,[],[f1942]) ).

fof(f1946,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(ennf_transformation,[],[f969]) ).

fof(f1947,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f970]) ).

fof(f1948,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ),
    inference(ennf_transformation,[],[f971]) ).

fof(f1949,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1)
      <=> X2 = X0 ) ),
    inference(ennf_transformation,[],[f972]) ).

fof(f1950,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1)
      <=> X2 = X0 ) ),
    inference(flattening,[],[f1949]) ).

fof(f1951,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(X2),X0) ),
    inference(ennf_transformation,[],[f973]) ).

fof(f1952,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(X2),X0) ),
    inference(flattening,[],[f1951]) ).

fof(f1953,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f974]) ).

fof(f1954,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
    inference(flattening,[],[f1953]) ).

fof(f1957,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ),
    inference(ennf_transformation,[],[f984]) ).

fof(f1958,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ),
    inference(flattening,[],[f1957]) ).

fof(f1959,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0
      | X1 = zero_zero_nat ),
    inference(ennf_transformation,[],[f986]) ).

fof(f1961,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f1003]) ).

fof(f1962,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f1004]) ).

fof(f1963,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f1005]) ).

fof(f1964,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(ennf_transformation,[],[f1006]) ).

fof(f1965,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(flattening,[],[f1964]) ).

fof(f1966,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | hAPP_nat_nat(plus_plus_nat(X2),X1) != hAPP_nat_nat(plus_plus_nat(X0),X3)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1007]) ).

fof(f1967,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | hAPP_nat_nat(plus_plus_nat(X2),X1) != hAPP_nat_nat(plus_plus_nat(X0),X3)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1966]) ).

fof(f1968,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(ennf_transformation,[],[f1008]) ).

fof(f1969,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X0 ),
    inference(ennf_transformation,[],[f1009]) ).

fof(f1971,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | X0 = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1014]) ).

fof(f1972,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | X0 = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f1971]) ).

fof(f1973,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1015]) ).

fof(f1974,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f1016]) ).

fof(f1975,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ),
    inference(flattening,[],[f1974]) ).

fof(f1976,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f1017]) ).

fof(f1977,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(flattening,[],[f1976]) ).

fof(f1978,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    inference(ennf_transformation,[],[f1019]) ).

fof(f1979,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    inference(flattening,[],[f1978]) ).

fof(f1980,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1020]) ).

fof(f1981,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(flattening,[],[f1980]) ).

fof(f1982,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f1025]) ).

fof(f1983,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(ennf_transformation,[],[f1026]) ).

fof(f1984,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(ennf_transformation,[],[f1027]) ).

fof(f1985,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(ennf_transformation,[],[f1028]) ).

fof(f1986,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(flattening,[],[f1985]) ).

fof(f1989,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    inference(ennf_transformation,[],[f1031]) ).

fof(f1990,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) ),
    inference(ennf_transformation,[],[f1032]) ).

fof(f1991,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1))) ),
    inference(ennf_transformation,[],[f1034]) ).

fof(f1992,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ),
    inference(ennf_transformation,[],[f1035]) ).

fof(f1994,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ) ),
    inference(ennf_transformation,[],[f1037]) ).

fof(f1997,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) ),
    inference(ennf_transformation,[],[f1040]) ).

fof(f1999,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X0) ),
    inference(ennf_transformation,[],[f1042]) ).

fof(f2000,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(ennf_transformation,[],[f1046]) ).

fof(f2001,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(flattening,[],[f2000]) ).

fof(f2004,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1055]) ).

fof(f2005,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(flattening,[],[f2004]) ).

fof(f2006,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
    <=> ( ! [X3] :
            ( hAPP_nat_nat(plus_plus_nat(X2),X3) != X1
            | hBOOL(hAPP_nat_bool(X0,X3)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          | hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
    inference(ennf_transformation,[],[f1057]) ).

fof(f2007,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
    <=> ( ! [X3] :
            ( hBOOL(hAPP_nat_bool(X0,X3))
            | hAPP_nat_nat(plus_plus_nat(X2),X3) != X1 )
        & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    inference(ennf_transformation,[],[f1058]) ).

fof(f2012,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != X0
      | X0 = zero_zero_nat
      | X1 = one_one_nat ),
    inference(ennf_transformation,[],[f1064]) ).

fof(f2013,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != X0
      | X0 = zero_zero_nat
      | X1 = one_one_nat ),
    inference(flattening,[],[f2012]) ).

fof(f2014,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1065]) ).

fof(f2015,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(flattening,[],[f2014]) ).

fof(f2018,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
    <=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    inference(ennf_transformation,[],[f1067]) ).

fof(f2019,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
    <=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
    inference(ennf_transformation,[],[f1068]) ).

fof(f2020,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2] :
          ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(X2),one_one_nat)))
          & ! [X3] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
              | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f1069]) ).

fof(f2021,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2] :
          ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(X2),one_one_nat)))
          & ! [X3] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
              | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ),
    inference(flattening,[],[f2020]) ).

fof(f2022,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ) ),
    inference(ennf_transformation,[],[f1070]) ).

fof(f2024,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1074]) ).

fof(f2025,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1076]) ).

fof(f2026,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1077]) ).

fof(f2027,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ) ),
    inference(ennf_transformation,[],[f1078]) ).

fof(f2028,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2) ),
    inference(ennf_transformation,[],[f1079]) ).

fof(f2029,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)
      <=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1) = X2 ) ),
    inference(ennf_transformation,[],[f1080]) ).

fof(f2030,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ) ),
    inference(ennf_transformation,[],[f1081]) ).

fof(f2031,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)) ),
    inference(ennf_transformation,[],[f1082]) ).

fof(f2032,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)
      <=> X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) ) ),
    inference(ennf_transformation,[],[f1083]) ).

fof(f2033,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ) ),
    inference(ennf_transformation,[],[f1084]) ).

fof(f2034,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X0))))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X0)))) ) ),
    inference(ennf_transformation,[],[f1085]) ).

fof(f2035,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      <=> ? [X1,X2] :
            ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) = X0
            & is_int(X2)
            & is_int(X1) ) ) ),
    inference(ennf_transformation,[],[f1086]) ).

fof(f2038,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | zero_zero_int = X2
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ) ),
    inference(ennf_transformation,[],[f1089]) ).

fof(f2039,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | zero_zero_int = X2
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ) ),
    inference(flattening,[],[f2038]) ).

fof(f2040,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(X1,X3))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X4] :
          ( ~ hBOOL(hAPP_int_bool(X1,X4))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(ennf_transformation,[],[f1232]) ).

fof(f2041,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(X1,X3))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X4] :
          ( ~ hBOOL(hAPP_int_bool(X1,X4))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(flattening,[],[f2040]) ).

fof(f2042,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(X1,X3))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X4] :
          ( ~ hBOOL(hAPP_int_bool(X1,X4))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(ennf_transformation,[],[f1233]) ).

fof(f2043,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(X1,X3))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X4] :
          ( ~ hBOOL(hAPP_int_bool(X1,X4))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X4),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(flattening,[],[f2042]) ).

fof(f2044,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ? [X1] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
          & hBOOL(hAPP_int_bool(zprime,X1))
          & is_int(X1) ) ),
    inference(ennf_transformation,[],[f1093]) ).

fof(f2045,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ? [X2] :
          ( ! [X3] :
              ( ~ is_int(X3)
              | ~ hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
              | X3 = X2 )
          & hBOOL(hAPP_int_bool(zcong(X0,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          & is_int(X2) ) ),
    inference(ennf_transformation,[],[f1094]) ).

fof(f2046,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ? [X2] :
          ( ! [X3] :
              ( ~ is_int(X3)
              | ~ hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
              | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
              | X3 = X2 )
          & hBOOL(hAPP_int_bool(zcong(X0,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          & is_int(X2) ) ),
    inference(flattening,[],[f2045]) ).

fof(f2047,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1095]) ).

fof(f2048,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),number_number_of_int(min)),X0)) ),
    inference(ennf_transformation,[],[f1096]) ).

fof(f2049,plain,
    ! [X0] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
        | zfact(X0) = hAPP_int_int(times_times_int(X0),zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
        | zfact(X0) = one_one_int ) ),
    inference(ennf_transformation,[],[f1097]) ).

fof(f2050,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | inv(X1,inv(X1,X0)) = X0 ),
    inference(ennf_transformation,[],[f1098]) ).

fof(f2051,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | inv(X1,inv(X1,X0)) = X0 ),
    inference(flattening,[],[f2050]) ).

fof(f2052,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ),
    inference(ennf_transformation,[],[f1099]) ).

fof(f2053,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ),
    inference(flattening,[],[f2052]) ).

fof(f2054,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X0)),X0)),X1),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3)) ),
    inference(ennf_transformation,[],[f1100]) ).

fof(f2056,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | X0 != inv(X1,X0) ),
    inference(ennf_transformation,[],[f1102]) ).

fof(f2057,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | X0 != inv(X1,X0) ),
    inference(flattening,[],[f2056]) ).

fof(f2058,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != one_one_int ),
    inference(ennf_transformation,[],[f1103]) ).

fof(f2059,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != one_one_int ),
    inference(flattening,[],[f2058]) ).

fof(f2060,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != hAPP_int_int(minus_minus_int(X1),one_one_int) ),
    inference(ennf_transformation,[],[f1104]) ).

fof(f2061,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != hAPP_int_int(minus_minus_int(X1),one_one_int) ),
    inference(flattening,[],[f2060]) ).

fof(f2062,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(X1,X0))) ),
    inference(ennf_transformation,[],[f1105]) ).

fof(f2063,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(X1,X0))) ),
    inference(flattening,[],[f2062]) ).

fof(f2064,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(X1,X0)),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(ennf_transformation,[],[f1106]) ).

fof(f2065,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(X1,X0)),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(flattening,[],[f2064]) ).

fof(f2066,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(multInv(X2,X0),multInv(X2,X1)),X2)) ),
    inference(ennf_transformation,[],[f1107]) ).

fof(f2067,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(multInv(X2,X0),multInv(X2,X1)),X2)) ),
    inference(flattening,[],[f2066]) ).

fof(f2068,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != zero_zero_int ),
    inference(ennf_transformation,[],[f1108]) ).

fof(f2069,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != zero_zero_int ),
    inference(flattening,[],[f2068]) ).

fof(f2070,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X3,X1)),hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3)) ),
    inference(ennf_transformation,[],[f1109]) ).

fof(f2071,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X3,X1)),hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3)) ),
    inference(flattening,[],[f2070]) ).

fof(f2072,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X2,X1),multInv(X2,X0)),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    inference(ennf_transformation,[],[f1110]) ).

fof(f2073,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X2,X1),multInv(X2,X0)),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    inference(flattening,[],[f2072]) ).

fof(f2074,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),X0),X1)) ),
    inference(ennf_transformation,[],[f1111]) ).

fof(f2075,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),X0),X1)) ),
    inference(flattening,[],[f2074]) ).

fof(f2076,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X1,X0),zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f1112]) ).

fof(f2077,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X1,X0),zero_zero_int),X1)) ),
    inference(flattening,[],[f2076]) ).

fof(f2078,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1)) ),
    inference(ennf_transformation,[],[f1113]) ).

fof(f2079,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1)) ),
    inference(flattening,[],[f2078]) ).

fof(f2080,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X2)),X2)),X0),hAPP_int_int(times_times_int(multInv(X3,X2)),X1)),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X3)) ),
    inference(ennf_transformation,[],[f1114]) ).

fof(f2081,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X2)),X2)),X0),hAPP_int_int(times_times_int(multInv(X3,X2)),X1)),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X3)) ),
    inference(flattening,[],[f2080]) ).

fof(f2082,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X2)),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),X1),X3)) ),
    inference(ennf_transformation,[],[f1115]) ).

fof(f2083,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X2)),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),X1),X3)) ),
    inference(flattening,[],[f2082]) ).

fof(f2084,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X0),multInv(X3,X1))),X3)) ),
    inference(ennf_transformation,[],[f1116]) ).

fof(f2085,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X0),multInv(X3,X1))),X3)) ),
    inference(flattening,[],[f2084]) ).

fof(f2086,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),multInv(X3,X0)),hAPP_int_int(times_times_int(X2),multInv(X3,X1))),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X3)) ),
    inference(ennf_transformation,[],[f1117]) ).

fof(f2087,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),multInv(X3,X0)),hAPP_int_int(times_times_int(X2),multInv(X3,X1))),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X3)) ),
    inference(flattening,[],[f2086]) ).

fof(f2088,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0))),X0),X1)) ),
    inference(ennf_transformation,[],[f1118]) ).

fof(f2089,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0))),X0),X1)) ),
    inference(flattening,[],[f2088]) ).

fof(f2090,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0)))),X1)) ),
    inference(ennf_transformation,[],[f1119]) ).

fof(f2091,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0)))),X1)) ),
    inference(flattening,[],[f2090]) ).

fof(f2094,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X0)),one_one_int),X1)) ),
    inference(ennf_transformation,[],[f1121]) ).

fof(f2095,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X0)),one_one_int),X1)) ),
    inference(flattening,[],[f2094]) ).

fof(f2096,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(member_int(inv(X2,X0),wset(X1,X2))) ),
    inference(ennf_transformation,[],[f1122]) ).

fof(f2097,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(member_int(inv(X2,X0),wset(X1,X2))) ),
    inference(flattening,[],[f2096]) ).

fof(f2098,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(inv(X2,X0),wset(X1,X2)))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(ennf_transformation,[],[f1123]) ).

fof(f2099,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(inv(X2,X0),wset(X1,X2)))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(flattening,[],[f2098]) ).

fof(f2100,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(member_int(X1,wset(X1,X0))) ),
    inference(ennf_transformation,[],[f1124]) ).

fof(f2101,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | hBOOL(member_int(X0,wset(X2,X1))) ),
    inference(ennf_transformation,[],[f1125]) ).

fof(f2102,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | hBOOL(member_int(X0,wset(X2,X1))) ),
    inference(flattening,[],[f2101]) ).

fof(f2103,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int))) ),
    inference(ennf_transformation,[],[f1126]) ).

fof(f2104,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int))) ),
    inference(flattening,[],[f2103]) ).

fof(f2105,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(ennf_transformation,[],[f1127]) ).

fof(f2106,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(flattening,[],[f2105]) ).

fof(f2107,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | ~ hBOOL(member_int(X0,wset(X2,X1)))
      | X0 = inv(X1,X2)
      | X0 = X2 ),
    inference(ennf_transformation,[],[f1128]) ).

fof(f2108,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | ~ hBOOL(member_int(X0,wset(X2,X1)))
      | X0 = inv(X1,X2)
      | X0 = X2 ),
    inference(flattening,[],[f2107]) ).

fof(f2109,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(ennf_transformation,[],[f1129]) ).

fof(f2110,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(flattening,[],[f2109]) ).

fof(f2111,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(ennf_transformation,[],[f1130]) ).

fof(f2112,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(flattening,[],[f2111]) ).

fof(f2113,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(ennf_transformation,[],[f1131]) ).

fof(f2114,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(flattening,[],[f2113]) ).

fof(f2115,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( is_int(X2)
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
            | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X2),one_one_int))) )
          & ~ hBOOL(hAPP_int_bool(X1,X2)) )
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(ennf_transformation,[],[f1132]) ).

fof(f2116,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( is_int(X2)
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
            | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X2),one_one_int))) )
          & ~ hBOOL(hAPP_int_bool(X1,X2)) )
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(flattening,[],[f2115]) ).

fof(f2117,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(ennf_transformation,[],[f1133]) ).

fof(f2118,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(flattening,[],[f2117]) ).

fof(f2119,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(ennf_transformation,[],[f1134]) ).

fof(f2120,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ? [X3] :
          ( is_int(X3)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
          & hBOOL(hAPP_int_bool(X0,X3))
          & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(flattening,[],[f2119]) ).

fof(f2121,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,X4))) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X2,X0)),X1)),hAPP_nat_nat(X2,hAPP_nat_nat(plus_plus_nat(X0),X1)))) ),
    inference(ennf_transformation,[],[f1135]) ).

fof(f2122,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls)))),X0) ),
    inference(ennf_transformation,[],[f1136]) ).

fof(f2123,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2] :
          ( hBOOL(hAPP_nat_bool(X1,X2))
          & ! [X3] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
              | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f1137]) ).

fof(f2124,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2] :
          ( hBOOL(hAPP_nat_bool(X1,X2))
          & ! [X3] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
              | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
    inference(flattening,[],[f2123]) ).

fof(f2126,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(member_int(X1,d22set(X0))) ),
    inference(ennf_transformation,[],[f1139]) ).

fof(f2127,plain,
    ! [X0,X1] :
      ( ~ hBOOL(member_int(X0,d22set(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(ennf_transformation,[],[f1140]) ).

fof(f2128,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(member_int(X1,d22set(X0))) ),
    inference(ennf_transformation,[],[f1141]) ).

fof(f2129,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(member_int(X1,d22set(X0))) ),
    inference(flattening,[],[f2128]) ).

fof(f2130,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ? [X2] :
          ( hAPP_nat_nat(plus_plus_nat(X0),X2) = X1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
    inference(ennf_transformation,[],[f1142]) ).

fof(f2135,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
      | X0 = one_one_nat ),
    inference(ennf_transformation,[],[f1153]) ).

fof(f2136,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(ennf_transformation,[],[f1154]) ).

fof(f2137,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(flattening,[],[f2136]) ).

fof(f2138,plain,
    ! [X0,X1,X2] :
      ( zero_zero_nat = X2
      | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1155]) ).

fof(f2139,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | zero_zero_nat = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    inference(ennf_transformation,[],[f1156]) ).

fof(f2140,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | zero_zero_nat = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    inference(flattening,[],[f2139]) ).

fof(f2141,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | X1 = zero_zero_nat
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1157]) ).

fof(f2142,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | X1 = zero_zero_nat
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(flattening,[],[f2141]) ).

fof(f2143,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | hAPP_nat_nat(times_times_nat(X2),X1) != hAPP_nat_nat(times_times_nat(X2),X0)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f1158]) ).

fof(f2144,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | hAPP_nat_nat(times_times_nat(X2),X1) != hAPP_nat_nat(times_times_nat(X2),X0)
      | X0 = X1 ),
    inference(flattening,[],[f2143]) ).

fof(f2145,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))),one_one_int) ),
    inference(ennf_transformation,[],[f1160]) ).

fof(f2146,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
        | hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
        | hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1)))),one_one_int) ) ),
    inference(ennf_transformation,[],[f1161]) ).

fof(f2149,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X1),X0))) ),
    inference(ennf_transformation,[],[f1165]) ).

fof(f2150,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X1),X0))) ),
    inference(flattening,[],[f2149]) ).

fof(f2151,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),X1)) ),
    inference(ennf_transformation,[],[f1166]) ).

fof(f2152,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int
      <=> ? [X2] :
            ( X0 = hAPP_int_int(times_times_int(X1),X2)
            & is_int(X2) ) ) ),
    inference(ennf_transformation,[],[f1167]) ).

fof(f2153,plain,
    ! [X0,X1,X2] :
      ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1)
      | hBOOL(hAPP_int_bool(zcong(X0,X2),X1)) ),
    inference(ennf_transformation,[],[f1169]) ).

fof(f2154,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1172]) ).

fof(f2155,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(flattening,[],[f2154]) ).

fof(f2156,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(div_mod_int(X2),X0))) ),
    inference(ennf_transformation,[],[f1173]) ).

fof(f2157,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(div_mod_int(X2),X0))) ),
    inference(flattening,[],[f2156]) ).

fof(f2158,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X0),X1)),X2) = hAPP_int_int(div_mod_int(X0),X2) ),
    inference(ennf_transformation,[],[f1182]) ).

fof(f2159,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X0),X1)),X2) = hAPP_int_int(div_mod_int(X0),X2) ),
    inference(flattening,[],[f2158]) ).

fof(f2163,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(ennf_transformation,[],[f1186]) ).

fof(f2164,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(flattening,[],[f2163]) ).

fof(f2166,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(div_mod_int(X0),X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),zero_zero_int)) ) ),
    inference(ennf_transformation,[],[f1188]) ).

fof(f2167,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(ennf_transformation,[],[f1189]) ).

fof(f2168,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(flattening,[],[f2167]) ).

fof(f2169,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X0)),zero_zero_int))
      | hAPP_int_int(div_mod_int(X1),X0) = hAPP_int_int(plus_plus_int(X1),X0) ),
    inference(ennf_transformation,[],[f1190]) ).

fof(f2170,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X0)),zero_zero_int))
      | hAPP_int_int(div_mod_int(X1),X0) = hAPP_int_int(plus_plus_int(X1),X0) ),
    inference(flattening,[],[f2169]) ).

fof(f2171,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      <=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
            | ! [X5,X6] :
                ( ~ is_int(X6)
                | ~ is_int(X5)
                | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) != X1
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
                | hBOOL(hAPP_int_bool(X0,X6)) ) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
            | ! [X3,X4] :
                ( ~ is_int(X4)
                | ~ is_int(X3)
                | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) != X1
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
                | hBOOL(hAPP_int_bool(X0,X4)) ) )
          & ( zero_zero_int != X2
            | hBOOL(hAPP_int_bool(X0,X1)) ) ) ) ),
    inference(ennf_transformation,[],[f1234]) ).

fof(f2172,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      <=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
            | ! [X5,X6] :
                ( ~ is_int(X6)
                | ~ is_int(X5)
                | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) != X1
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
                | hBOOL(hAPP_int_bool(X0,X6)) ) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
            | ! [X3,X4] :
                ( ~ is_int(X4)
                | ~ is_int(X3)
                | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) != X1
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
                | hBOOL(hAPP_int_bool(X0,X4)) ) )
          & ( zero_zero_int != X2
            | hBOOL(hAPP_int_bool(X0,X1)) ) ) ) ),
    inference(flattening,[],[f2171]) ).

fof(f2173,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(ennf_transformation,[],[f1193]) ).

fof(f2174,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(flattening,[],[f2173]) ).

fof(f2175,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),hAPP_int_int(times_times_int(X1),X3))) ),
    inference(ennf_transformation,[],[f1194]) ).

fof(f2176,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),hAPP_int_int(times_times_int(X1),X3))) ),
    inference(flattening,[],[f2175]) ).

fof(f2177,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(ennf_transformation,[],[f1195]) ).

fof(f2178,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(flattening,[],[f2177]) ).

fof(f2179,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),zero_zero_int)) ),
    inference(ennf_transformation,[],[f1196]) ).

fof(f2180,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),zero_zero_int)) ),
    inference(flattening,[],[f2179]) ).

fof(f2181,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),zero_zero_int))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ) )
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ) )
      | zero_zero_int = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(ennf_transformation,[],[f1197]) ).

fof(f2182,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),zero_zero_int))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ) )
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ) )
      | zero_zero_int = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(flattening,[],[f2181]) ).

fof(f2183,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) = hAPP_int_int(minus_minus_int(X0),one_one_int) ),
    inference(ennf_transformation,[],[f1199]) ).

fof(f2184,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(ennf_transformation,[],[f1200]) ).

fof(f2185,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | ? [X2] :
          ( X0 = hAPP_int_int(times_times_int(X1),X2)
          & is_int(X2) ) ),
    inference(ennf_transformation,[],[f1201]) ).

fof(f2186,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | ? [X2] :
          ( X0 = hAPP_int_int(times_times_int(X1),X2)
          & is_int(X2) ) ),
    inference(flattening,[],[f2185]) ).

fof(f2187,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(X2,X0)),standardRes(X2,X1)),hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(ennf_transformation,[],[f1202]) ).

fof(f2188,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    inference(ennf_transformation,[],[f1203]) ).

fof(f2189,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    inference(ennf_transformation,[],[f1204]) ).

fof(f2191,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | hAPP_nat_nat(div_mod_nat(X0),X1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X1) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ) ),
    inference(ennf_transformation,[],[f1207]) ).

fof(f2192,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(div_mod_nat(X1),X0) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X0) ),
    inference(ennf_transformation,[],[f1209]) ).

fof(f2193,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ),
    inference(ennf_transformation,[],[f1213]) ).

fof(f2194,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(X1,X0)),X1)) ),
    inference(ennf_transformation,[],[f1218]) ).

fof(f2195,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(member_int(X0,sr(X1)))
      | standardRes(X1,X0) = X0 ),
    inference(ennf_transformation,[],[f1219]) ).

fof(f2196,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(member_int(X0,sr(X1)))
      | standardRes(X1,X0) = X0 ),
    inference(flattening,[],[f2195]) ).

fof(f2197,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
    <=> ( ( zero_zero_nat = X2
          | ! [X3,X4] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) != X1
              | hBOOL(hAPP_nat_bool(X0,X4)) ) )
        & ( zero_zero_nat != X2
          | hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
    inference(ennf_transformation,[],[f1220]) ).

fof(f2198,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
    <=> ( ( zero_zero_nat = X2
          | ! [X3,X4] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) != X1
              | hBOOL(hAPP_nat_bool(X0,X4)) ) )
        & ( zero_zero_nat != X2
          | hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
    inference(flattening,[],[f2197]) ).

fof(f2199,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X3))),X1)),hAPP_nat_nat(times_times_nat(X2),X3))) ),
    inference(ennf_transformation,[],[f1221]) ).

fof(f2200,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X3))),X1)),hAPP_nat_nat(times_times_nat(X2),X3))) ),
    inference(flattening,[],[f2199]) ).

fof(f2201,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(X1,X0))) ),
    inference(ennf_transformation,[],[f1222]) ).

fof(f2202,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( standardRes(X2,X0) = standardRes(X2,X1)
      <=> hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
    inference(ennf_transformation,[],[f1223]) ).

fof(f2203,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
    inference(ennf_transformation,[],[f1231]) ).

fof(f2213,plain,
    ( one_one_int != t
    | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(bit0(bit1(pls)))))
      & is_int(sK6)
      & is_int(sK5) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f1251]) ).

fof(f2214,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(bit0(bit1(pls)))))
      & is_int(sK8)
      & is_int(sK7) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f1252]) ).

fof(f2215,plain,
    ( is_int(sK9)
    & hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),sK9) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f1253]) ).

fof(f2219,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f2220,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
        | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0))) )
      & ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f2222,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f2224,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f2226,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit1(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit1(X1))) ) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f2228,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit1(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit1(X1))) ) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f2230,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit0(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit0(X1))) ) ),
    inference(nnf_transformation,[],[f95]) ).

fof(f2232,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit0(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit0(X1))) ) ),
    inference(nnf_transformation,[],[f98]) ).

fof(f2233,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ) ),
    inference(nnf_transformation,[],[f99]) ).

fof(f2234,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f2235,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f2236,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f107]) ).

fof(f2238,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit0(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit0(X1))) ) ),
    inference(nnf_transformation,[],[f109]) ).

fof(f2240,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit1(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit1(X1))) ) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f2241,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1)) ) ),
    inference(nnf_transformation,[],[f113]) ).

fof(f2242,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ) ),
    inference(nnf_transformation,[],[f114]) ).

fof(f2243,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(member_int(X0,X1))
        | hBOOL(hAPP_int_bool(X1,X0)) )
      & ( ~ hBOOL(hAPP_int_bool(X1,X0))
        | hBOOL(member_int(X0,X1)) ) ),
    inference(nnf_transformation,[],[f144]) ).

fof(f2244,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( number_number_of_int(X0) != number_number_of_int(X1)
          | X0 = X1 )
        & ( X0 != X1
          | number_number_of_int(X0) = number_number_of_int(X1) ) ) ),
    inference(nnf_transformation,[],[f1272]) ).

fof(f2245,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( number267125858f_real(X0) != number267125858f_real(X1)
          | X0 = X1 )
        & ( X0 != X1
          | number267125858f_real(X0) = number267125858f_real(X1) ) ) ),
    inference(nnf_transformation,[],[f1274]) ).

fof(f2249,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( bit1(X0) != bit1(X1)
          | X0 = X1 )
        & ( X0 != X1
          | bit1(X0) = bit1(X1) ) ) ),
    inference(nnf_transformation,[],[f1277]) ).

fof(f2250,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( bit0(X0) != bit0(X1)
          | X0 = X1 )
        & ( X0 != X1
          | bit0(X0) = bit0(X1) ) ) ),
    inference(nnf_transformation,[],[f1279]) ).

fof(f2253,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit0(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit0(X1))) ) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f2255,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X0))) ) ),
    inference(nnf_transformation,[],[f178]) ).

fof(f2256,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f179]) ).

fof(f2258,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit1(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit1(X1))) ) ),
    inference(nnf_transformation,[],[f181]) ).

fof(f2259,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),pls)) ) ),
    inference(nnf_transformation,[],[f182]) ).

fof(f2260,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X0))) ) ),
    inference(nnf_transformation,[],[f183]) ).

fof(f2263,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ) ),
    inference(nnf_transformation,[],[f188]) ).

fof(f2264,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls)))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ) ),
    inference(nnf_transformation,[],[f189]) ).

fof(f2265,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ) ),
    inference(nnf_transformation,[],[f190]) ).

fof(f2266,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ) ),
    inference(nnf_transformation,[],[f191]) ).

fof(f2267,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int)) ) ),
    inference(nnf_transformation,[],[f192]) ).

fof(f2268,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls)))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ) ),
    inference(nnf_transformation,[],[f193]) ).

fof(f2269,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ) ),
    inference(nnf_transformation,[],[f194]) ).

fof(f2270,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ) ),
    inference(nnf_transformation,[],[f195]) ).

fof(f2277,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( X0 = X1
          | X2 = X3
          | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) )
        & ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0))
          | ( X0 != X1
            & X2 != X3 ) ) ) ),
    inference(nnf_transformation,[],[f1286]) ).

fof(f2278,plain,
    ! [X0,X1,X2,X3] :
      ( ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( X0 = X1
          | X2 = X3
          | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) )
        & ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0))
          | ( X0 != X1
            & X2 != X3 ) ) ) ),
    inference(flattening,[],[f2277]) ).

fof(f2279,plain,
    ! [X0,X1,X2,X3] :
      ( ( X0 = X1
        | X2 = X3
        | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0)) )
      & ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0))
        | ( X0 != X1
          & X2 != X3 ) ) ),
    inference(nnf_transformation,[],[f206]) ).

fof(f2280,plain,
    ! [X0,X1,X2,X3] :
      ( ( X0 = X1
        | X2 = X3
        | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0)) )
      & ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0))
        | ( X0 != X1
          & X2 != X3 ) ) ),
    inference(flattening,[],[f2279]) ).

fof(f2281,plain,
    ! [X0,X1,X2,X3] :
      ( ( X0 = X1
        | X2 = X3
        | hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0)) )
      & ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0))
        | ( X0 != X1
          & X2 != X3 ) ) ),
    inference(nnf_transformation,[],[f207]) ).

fof(f2282,plain,
    ! [X0,X1,X2,X3] :
      ( ( X0 = X1
        | X2 = X3
        | hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0)) )
      & ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0))
        | ( X0 != X1
          & X2 != X3 ) ) ),
    inference(flattening,[],[f2281]) ).

fof(f2285,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1325]) ).

fof(f2286,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1326]) ).

fof(f2287,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1327]) ).

fof(f2288,plain,
    ( ! [X1] :
        ( ~ is_int(X1)
        | ~ hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
        | sK10 = X1 )
    & hBOOL(hAPP_int_bool(zcong(s1,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK10))
    & is_int(sK10) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f1329]) ).

fof(f2289,plain,
    ( is_int(sK11)
    & hBOOL(hAPP_int_bool(zcong(s1,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
    & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK11)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f1331]) ).

fof(f2296,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( hAPP_int_int(plus_plus_int(X0),X1) != X0
          | X1 = zero_zero_int )
        & ( zero_zero_int != X1
          | X0 = hAPP_int_int(plus_plus_int(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f1380]) ).

fof(f2298,plain,
    ! [X0,X1] :
      ( ( hAPP_real_real(plus_plus_real(X0),X1) != X0
        | X1 = zero_zero_real )
      & ( zero_zero_real != X1
        | X0 = hAPP_real_real(plus_plus_real(X0),X1) ) ),
    inference(nnf_transformation,[],[f381]) ).

fof(f2299,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(plus_plus_int(X0),X0)
          | X0 = zero_zero_int )
        & ( zero_zero_int != X0
          | hAPP_int_int(plus_plus_int(X0),X0) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f1381]) ).

fof(f2300,plain,
    ! [X0] :
      ( ( hAPP_real_real(plus_plus_real(X0),X0) != zero_zero_real
        | X0 = zero_zero_real )
      & ( zero_zero_real != X0
        | hAPP_real_real(plus_plus_real(X0),X0) = zero_zero_real ) ),
    inference(nnf_transformation,[],[f383]) ).

fof(f2301,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2))))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(nnf_transformation,[],[f398]) ).

fof(f2302,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X4))
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2)))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2))) )
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2)))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2))) ) ) ),
    inference(nnf_transformation,[],[f1397]) ).

fof(f2304,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
      & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f410]) ).

fof(f2305,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f1417]) ).

fof(f2306,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) = zero_zero_int ) ) ),
    inference(flattening,[],[f2305]) ).

fof(f2310,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f426]) ).

fof(f2311,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)) ) ) ),
    inference(nnf_transformation,[],[f1441]) ).

fof(f2312,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)) ) ) ),
    inference(flattening,[],[f2311]) ).

fof(f2313,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f440]) ).

fof(f2314,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)) ) ),
    inference(flattening,[],[f2313]) ).

fof(f2315,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
            | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ) ),
    inference(nnf_transformation,[],[f1442]) ).

fof(f2316,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
            | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ) ),
    inference(flattening,[],[f2315]) ).

fof(f2317,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
          | X1 != zero_zero_int
          | X0 != zero_zero_int )
        & ( ( zero_zero_int = X1
            & zero_zero_int = X0 )
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ) ) ),
    inference(nnf_transformation,[],[f1444]) ).

fof(f2318,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
          | X1 != zero_zero_int
          | X0 != zero_zero_int )
        & ( ( zero_zero_int = X1
            & zero_zero_int = X0 )
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ) ) ),
    inference(flattening,[],[f2317]) ).

fof(f2319,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))))
        | X1 != zero_zero_real
        | X0 != zero_zero_real )
      & ( ( zero_zero_real = X1
          & zero_zero_real = X0 )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))) ) ),
    inference(nnf_transformation,[],[f445]) ).

fof(f2320,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))))
        | X1 != zero_zero_real
        | X0 != zero_zero_real )
      & ( ( zero_zero_real = X1
          & zero_zero_real = X0 )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))) ) ),
    inference(flattening,[],[f2319]) ).

fof(f2321,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ) ),
    inference(nnf_transformation,[],[f1445]) ).

fof(f2322,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ) ),
    inference(flattening,[],[f2321]) ).

fof(f2323,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
    inference(nnf_transformation,[],[f452]) ).

fof(f2324,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ( ( one_one_int != hAPP_int_int(times_times_int(X1),X0)
          | ( X0 = one_one_int
            & X1 = one_one_int ) )
        & ( one_one_int != X0
          | one_one_int != X1
          | hAPP_int_int(times_times_int(X1),X0) = one_one_int ) ) ),
    inference(nnf_transformation,[],[f1448]) ).

fof(f2325,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ( ( one_one_int != hAPP_int_int(times_times_int(X1),X0)
          | ( X0 = one_one_int
            & X1 = one_one_int ) )
        & ( one_one_int != X0
          | one_one_int != X1
          | hAPP_int_int(times_times_int(X1),X0) = one_one_int ) ) ),
    inference(flattening,[],[f2324]) ).

fof(f2326,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f454]) ).

fof(f2327,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0))) ) ),
    inference(nnf_transformation,[],[f455]) ).

fof(f2328,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ) ),
    inference(nnf_transformation,[],[f456]) ).

fof(f2329,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f457]) ).

fof(f2330,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f458]) ).

fof(f2331,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ) ),
    inference(nnf_transformation,[],[f459]) ).

fof(f2332,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0))) ) ),
    inference(nnf_transformation,[],[f460]) ).

fof(f2333,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f461]) ).

fof(f2334,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f462]) ).

fof(f2337,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))))
        | X0 != zero_zero_real )
      & ( zero_zero_real = X0
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))))) ) ),
    inference(nnf_transformation,[],[f479]) ).

fof(f2338,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))))
          | X0 != zero_zero_int )
        & ( zero_zero_int = X0
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))) ) ) ),
    inference(nnf_transformation,[],[f1463]) ).

fof(f2341,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f1465]) ).

fof(f2342,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int ) ) ),
    inference(flattening,[],[f2341]) ).

fof(f2343,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f503]) ).

fof(f2344,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
    inference(flattening,[],[f2343]) ).

fof(f2345,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ) ) ),
    inference(nnf_transformation,[],[f1473]) ).

fof(f2346,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
          | ( X1 = zero_zero_int
            & X0 = zero_zero_int ) )
        & ( zero_zero_int != X1
          | zero_zero_int != X0
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ) ) ),
    inference(flattening,[],[f2345]) ).

fof(f2347,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))))
        | X1 != zero_zero_real
        | X0 != zero_zero_real )
      & ( ( zero_zero_real = X1
          & zero_zero_real = X0 )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ) ),
    inference(nnf_transformation,[],[f507]) ).

fof(f2348,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))))
        | X1 != zero_zero_real
        | X0 != zero_zero_real )
      & ( ( zero_zero_real = X1
          & zero_zero_real = X0 )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ) ),
    inference(flattening,[],[f2347]) ).

fof(f2349,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
          | X1 != zero_zero_int
          | X0 != zero_zero_int )
        & ( ( zero_zero_int = X1
            & zero_zero_int = X0 )
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ) ) ),
    inference(nnf_transformation,[],[f1475]) ).

fof(f2350,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
          | X1 != zero_zero_int
          | X0 != zero_zero_int )
        & ( ( zero_zero_int = X1
            & zero_zero_int = X0 )
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ) ) ),
    inference(flattening,[],[f2349]) ).

fof(f2351,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ( ( hAPP_nat_real(power_power_real(X2),X0) != hAPP_nat_real(power_power_real(X2),X1)
          | X0 = X1 )
        & ( X0 != X1
          | hAPP_nat_real(power_power_real(X2),X0) = hAPP_nat_real(power_power_real(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f1485]) ).

fof(f2352,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ( ( hAPP_nat_nat(power_power_nat(X2),X0) != hAPP_nat_nat(power_power_nat(X2),X1)
          | X0 = X1 )
        & ( X0 != X1
          | hAPP_nat_nat(power_power_nat(X2),X0) = hAPP_nat_nat(power_power_nat(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f1486]) ).

fof(f2353,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ( ( hAPP_nat_int(power_power_int(X2),X0) != hAPP_nat_int(power_power_int(X2),X1)
          | X0 = X1 )
        & ( X0 != X1
          | hAPP_nat_int(power_power_int(X2),X0) = hAPP_nat_int(power_power_int(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f1487]) ).

fof(f2357,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(zprime,X0))
          | ( ! [X1] :
                ( ~ is_int(X1)
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
                | X1 = X0
                | X1 = one_one_int )
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
        & ( ? [X1] :
              ( is_int(X1)
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
              & X0 != X1
              & one_one_int != X1 )
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
          | hBOOL(hAPP_int_bool(zprime,X0)) ) ) ),
    inference(nnf_transformation,[],[f1511]) ).

fof(f2358,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(zprime,X0))
          | ( ! [X1] :
                ( ~ is_int(X1)
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
                | X1 = X0
                | X1 = one_one_int )
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
        & ( ? [X1] :
              ( is_int(X1)
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
              & X0 != X1
              & one_one_int != X1 )
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
          | hBOOL(hAPP_int_bool(zprime,X0)) ) ) ),
    inference(flattening,[],[f2357]) ).

fof(f2359,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(zprime,X0))
          | ( ! [X2] :
                ( ~ is_int(X2)
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
                | X0 = X2
                | one_one_int = X2 )
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
        & ( ? [X1] :
              ( is_int(X1)
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
              & X0 != X1
              & one_one_int != X1 )
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
          | hBOOL(hAPP_int_bool(zprime,X0)) ) ) ),
    inference(rectify,[],[f2358]) ).

fof(f2360,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(zprime,X0))
          | ( ! [X2] :
                ( ~ is_int(X2)
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
                | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
                | X0 = X2
                | one_one_int = X2 )
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
        & ( ( is_int(sK12(X0))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK12(X0)),X0))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK12(X0)))
            & sK12(X0) != X0
            & one_one_int != sK12(X0) )
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
          | hBOOL(hAPP_int_bool(zprime,X0)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f2359]) ).

fof(f2361,plain,
    ( is_int(sK13)
    & hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK13),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f1516]) ).

fof(f2362,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
        | X1 = zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( zero_zero_nat != X1
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ) ),
    inference(nnf_transformation,[],[f540]) ).

fof(f2363,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
        | X1 = zero_zero_nat
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( zero_zero_nat != X1
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ) ),
    inference(flattening,[],[f2362]) ).

fof(f2364,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | X1 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & zero_zero_nat != X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ) ),
    inference(nnf_transformation,[],[f541]) ).

fof(f2365,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | X1 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & zero_zero_nat != X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ) ),
    inference(flattening,[],[f2364]) ).

fof(f2366,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | number_number_of_nat(X1) = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & number_number_of_nat(X1) != zero_zero_nat )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)))) ) ),
    inference(nnf_transformation,[],[f542]) ).

fof(f2367,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | number_number_of_nat(X1) = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & number_number_of_nat(X1) != zero_zero_nat )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)))) ) ),
    inference(flattening,[],[f2366]) ).

fof(f2368,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( bit1(X0) != min
          | X0 = min )
        & ( min != X0
          | bit1(X0) = min ) ) ),
    inference(nnf_transformation,[],[f1519]) ).

fof(f2370,plain,
    ! [X0] :
      ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
        | X0 = zero_zero_real )
      & ( zero_zero_real != X0
        | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0))) ) ),
    inference(nnf_transformation,[],[f553]) ).

fof(f2371,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),min)) ) ),
    inference(nnf_transformation,[],[f554]) ).

fof(f2372,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f555]) ).

fof(f2373,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(X0))) ) ),
    inference(nnf_transformation,[],[f558]) ).

fof(f2374,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),min)) ) ),
    inference(nnf_transformation,[],[f560]) ).

fof(f2375,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f561]) ).

fof(f2376,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),min)) ) ),
    inference(nnf_transformation,[],[f564]) ).

fof(f2377,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(X0))) ) ),
    inference(nnf_transformation,[],[f575]) ).

fof(f2378,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),min)) ) ),
    inference(nnf_transformation,[],[f576]) ).

fof(f2379,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( one_one_int != hAPP_int_int(times_times_int(X0),X1)
          | ( X1 = number_number_of_int(min)
            & X0 = number_number_of_int(min) )
          | ( X1 = one_one_int
            & X0 = one_one_int ) )
        & ( ( ( number_number_of_int(min) != X1
              | number_number_of_int(min) != X0 )
            & ( one_one_int != X1
              | one_one_int != X0 ) )
          | hAPP_int_int(times_times_int(X0),X1) = one_one_int ) ) ),
    inference(nnf_transformation,[],[f1526]) ).

fof(f2380,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( one_one_int != hAPP_int_int(times_times_int(X0),X1)
          | ( X1 = number_number_of_int(min)
            & X0 = number_number_of_int(min) )
          | ( X1 = one_one_int
            & X0 = one_one_int ) )
        & ( ( ( number_number_of_int(min) != X1
              | number_number_of_int(min) != X0 )
            & ( one_one_int != X1
              | one_one_int != X0 ) )
          | hAPP_int_int(times_times_int(X0),X1) = one_one_int ) ) ),
    inference(flattening,[],[f2379]) ).

fof(f2381,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ) ),
    inference(nnf_transformation,[],[f585]) ).

fof(f2383,plain,
    ! [X0] :
      ( ( number_number_of_nat(X0) != zero_zero_nat
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
        | zero_zero_nat = number_number_of_nat(X0) ) ),
    inference(nnf_transformation,[],[f587]) ).

fof(f2384,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
        | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) )
      & ( ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X2))
        | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
    inference(nnf_transformation,[],[f588]) ).

fof(f2385,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
          | X0 = X1 )
        & ( X0 != X1
          | hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int)) ) ) ),
    inference(nnf_transformation,[],[f1549]) ).

fof(f2386,plain,
    ! [X0,X1] :
      ( ( zero_zero_real != hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1))
        | ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_real ) )
      & ( number_number_of_nat(X1) = zero_zero_nat
        | zero_zero_real != X0
        | hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1)) = zero_zero_real ) ),
    inference(nnf_transformation,[],[f608]) ).

fof(f2387,plain,
    ! [X0,X1] :
      ( ( zero_zero_real != hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1))
        | ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_real ) )
      & ( number_number_of_nat(X1) = zero_zero_nat
        | zero_zero_real != X0
        | hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1)) = zero_zero_real ) ),
    inference(flattening,[],[f2386]) ).

fof(f2388,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))
        | ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_nat ) )
      & ( number_number_of_nat(X1) = zero_zero_nat
        | zero_zero_nat != X0
        | hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f609]) ).

fof(f2389,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))
        | ( number_number_of_nat(X1) != zero_zero_nat
          & X0 = zero_zero_nat ) )
      & ( number_number_of_nat(X1) = zero_zero_nat
        | zero_zero_nat != X0
        | hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)) = zero_zero_nat ) ),
    inference(flattening,[],[f2388]) ).

fof(f2390,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1))
          | ( number_number_of_nat(X1) != zero_zero_nat
            & X0 = zero_zero_int ) )
        & ( number_number_of_nat(X1) = zero_zero_nat
          | zero_zero_int != X0
          | hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1)) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f1556]) ).

fof(f2391,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1))
          | ( number_number_of_nat(X1) != zero_zero_nat
            & X0 = zero_zero_int ) )
        & ( number_number_of_nat(X1) = zero_zero_nat
          | zero_zero_int != X0
          | hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1)) = zero_zero_int ) ) ),
    inference(flattening,[],[f2390]) ).

fof(f2392,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X1)
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
          | ? [X3] :
              ( X1 = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3))
              & is_int(X3) ) )
        & ( ! [X3] :
              ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3)) != X1
              | ~ is_int(X3) )
          | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ) ),
    inference(nnf_transformation,[],[f1564]) ).

fof(f2393,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X1)
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
          | ? [X4] :
              ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X4)) = X1
              & is_int(X4) ) )
        & ( ! [X3] :
              ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3)) != X1
              | ~ is_int(X3) )
          | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ) ),
    inference(rectify,[],[f2392]) ).

fof(f2394,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X1)
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
          | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),sK14(X0,X1,X2))) = X1
            & is_int(sK14(X0,X1,X2)) ) )
        & ( ! [X3] :
              ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3)) != X1
              | ~ is_int(X3) )
          | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X4,sK14(X0,X1,X2))],[f2393]) ).

fof(f2395,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),zero_zero_int)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),zero_zero_int))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f653]) ).

fof(f2396,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1)))
        | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
    inference(nnf_transformation,[],[f655]) ).

fof(f2397,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ) ),
    inference(nnf_transformation,[],[f659]) ).

fof(f2398,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1))
        | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1)) )
      & ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
        | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1)) ) ),
    inference(nnf_transformation,[],[f663]) ).

fof(f2399,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4))
          | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4)) )
        & ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4))
          | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4)) ) ) ),
    inference(nnf_transformation,[],[f1607]) ).

fof(f2400,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4))
          | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4)) )
        & ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4))
          | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4)) ) ) ),
    inference(nnf_transformation,[],[f1608]) ).

fof(f2402,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
        | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ) ),
    inference(nnf_transformation,[],[f682]) ).

fof(f2403,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
        | ? [X2] :
            ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
            & is_int(X2) ) )
      & ( ! [X2] :
            ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
            | ~ is_int(X2) )
        | hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
    inference(nnf_transformation,[],[f694]) ).

fof(f2404,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
        | ? [X3] :
            ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
            & is_int(X3) ) )
      & ( ! [X2] :
            ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
            | ~ is_int(X2) )
        | hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
    inference(rectify,[],[f2403]) ).

fof(f2405,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
        | ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
          & is_int(sK15(X0,X1)) ) )
      & ( ! [X2] :
            ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
            | ~ is_int(X2) )
        | hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X0,X1))],[f2404]) ).

fof(f2406,plain,
    ! [X0,X1] :
      ( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ) ),
    inference(nnf_transformation,[],[f695]) ).

fof(f2407,plain,
    ! [X0,X1] :
      ( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ) ),
    inference(flattening,[],[f2406]) ).

fof(f2408,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real)) )
      & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
    inference(nnf_transformation,[],[f701]) ).

fof(f2411,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
        | ( X0 != X1
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) )
      & ( X0 = X1
        | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    inference(nnf_transformation,[],[f712]) ).

fof(f2412,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
        | ( X0 != X1
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) )
      & ( X0 = X1
        | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
    inference(flattening,[],[f2411]) ).

fof(f2415,plain,
    ! [X0,X1] :
      ( ( hAPP_real_real(times_times_real(X0),X1) != zero_zero_real
        | X1 = zero_zero_real
        | X0 = zero_zero_real )
      & ( ( zero_zero_real != X1
          & zero_zero_real != X0 )
        | hAPP_real_real(times_times_real(X0),X1) = zero_zero_real ) ),
    inference(nnf_transformation,[],[f730]) ).

fof(f2416,plain,
    ! [X0,X1] :
      ( ( hAPP_real_real(times_times_real(X0),X1) != zero_zero_real
        | X1 = zero_zero_real
        | X0 = zero_zero_real )
      & ( ( zero_zero_real != X1
          & zero_zero_real != X0 )
        | hAPP_real_real(times_times_real(X0),X1) = zero_zero_real ) ),
    inference(flattening,[],[f2415]) ).

fof(f2417,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(times_times_int(X0),X1)
          | X1 = zero_zero_int
          | X0 = zero_zero_int )
        & ( ( zero_zero_int != X1
            & zero_zero_int != X0 )
          | hAPP_int_int(times_times_int(X0),X1) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f1668]) ).

fof(f2418,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(times_times_int(X0),X1)
          | X1 = zero_zero_int
          | X0 = zero_zero_int )
        & ( ( zero_zero_int != X1
            & zero_zero_int != X0 )
          | hAPP_int_int(times_times_int(X0),X1) = zero_zero_int ) ) ),
    inference(flattening,[],[f2417]) ).

fof(f2419,plain,
    ! [X0,X1,X2] :
      ( zero_zero_real = X2
      | ( ( hAPP_real_real(times_times_real(X0),X2) != hAPP_real_real(times_times_real(X1),X2)
          | X0 = X1 )
        & ( X0 != X1
          | hAPP_real_real(times_times_real(X0),X2) = hAPP_real_real(times_times_real(X1),X2) ) ) ),
    inference(nnf_transformation,[],[f1704]) ).

fof(f2420,plain,
    ! [X0,X1,X2] :
      ( zero_zero_real = X2
      | ( ( hAPP_real_real(times_times_real(X2),X1) != hAPP_real_real(times_times_real(X2),X0)
          | X0 = X1 )
        & ( X0 != X1
          | hAPP_real_real(times_times_real(X2),X0) = hAPP_real_real(times_times_real(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f1705]) ).

fof(f2423,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(power_power_nat(X0),X1) != zero_zero_nat
        | ( X0 = zero_zero_nat
          & X1 != zero_zero_nat ) )
      & ( zero_zero_nat != X0
        | zero_zero_nat = X1
        | hAPP_nat_nat(power_power_nat(X0),X1) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f794]) ).

fof(f2424,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(power_power_nat(X0),X1) != zero_zero_nat
        | ( X0 = zero_zero_nat
          & X1 != zero_zero_nat ) )
      & ( zero_zero_nat != X0
        | zero_zero_nat = X1
        | hAPP_nat_nat(power_power_nat(X0),X1) = zero_zero_nat ) ),
    inference(flattening,[],[f2423]) ).

fof(f2425,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ) ),
    inference(nnf_transformation,[],[f834]) ).

fof(f2426,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ) ),
    inference(flattening,[],[f2425]) ).

fof(f2427,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f835]) ).

fof(f2428,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int)) ) ),
    inference(flattening,[],[f2427]) ).

fof(f2429,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ) ),
    inference(nnf_transformation,[],[f836]) ).

fof(f2430,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ) ),
    inference(flattening,[],[f2429]) ).

fof(f2431,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1))) ) ),
    inference(nnf_transformation,[],[f837]) ).

fof(f2432,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1))) ) ),
    inference(flattening,[],[f2431]) ).

fof(f2433,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) )
        & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1818]) ).

fof(f2434,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) )
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1819]) ).

fof(f2435,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) )
        & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1850]) ).

fof(f2436,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1851]) ).

fof(f2437,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ) ),
    inference(nnf_transformation,[],[f877]) ).

fof(f2438,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ) ),
    inference(flattening,[],[f2437]) ).

fof(f2439,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ) ),
    inference(nnf_transformation,[],[f878]) ).

fof(f2440,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ) ),
    inference(flattening,[],[f2439]) ).

fof(f2441,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ) ),
    inference(nnf_transformation,[],[f879]) ).

fof(f2442,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) )
        | ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
          & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) )
      & ( ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) )
          & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ) )
        | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ) ),
    inference(flattening,[],[f2441]) ).

fof(f2443,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ) ),
    inference(nnf_transformation,[],[f880]) ).

fof(f2444,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
        | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ) )
      & ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
          & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ) ),
    inference(flattening,[],[f2443]) ).

fof(f2445,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
        | X1 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
          & zero_zero_nat != X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(nnf_transformation,[],[f886]) ).

fof(f2446,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
        | X1 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
          & zero_zero_nat != X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(flattening,[],[f2445]) ).

fof(f2447,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) )
        & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2))) ) ) ),
    inference(nnf_transformation,[],[f1858]) ).

fof(f2448,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
        & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2))) ) ) ),
    inference(nnf_transformation,[],[f1859]) ).

fof(f2449,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
        & ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
          | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1860]) ).

fof(f2450,plain,
    ! [X0,X1] :
      ( ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) = zero_zero_real ) ),
    inference(nnf_transformation,[],[f892]) ).

fof(f2451,plain,
    ! [X0,X1] :
      ( ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))
        | ( X1 = zero_zero_real
          & X0 = zero_zero_real ) )
      & ( zero_zero_real != X1
        | zero_zero_real != X0
        | hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) = zero_zero_real ) ),
    inference(flattening,[],[f2450]) ).

fof(f2452,plain,
    ! [X0,X1] :
      ( ( one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1)
        | X1 = zero_zero_nat
        | X0 = one_one_nat )
      & ( ( zero_zero_nat != X1
          & one_one_nat != X0 )
        | hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat ) ),
    inference(nnf_transformation,[],[f895]) ).

fof(f2453,plain,
    ! [X0,X1] :
      ( ( one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1)
        | X1 = zero_zero_nat
        | X0 = one_one_nat )
      & ( ( zero_zero_nat != X1
          & one_one_nat != X0 )
        | hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat ) ),
    inference(flattening,[],[f2452]) ).

fof(f2454,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ( hAPP_nat_real(power_power_real(sK16(X0,X1)),X1) = X0
        & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK16(X0,X1))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f1872]) ).

fof(f2455,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ( ! [X3] :
            ( hAPP_nat_real(power_power_real(X3),X1) != X0
            | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
            | sK17(X0,X1) = X3 )
        & hAPP_nat_real(power_power_real(sK17(X0,X1)),X1) = X0
        & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK17(X0,X1))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f1874]) ).

fof(f2456,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1))
          | X0 = one_one_nat )
        & ( one_one_nat != X0
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1)) ) ) ),
    inference(nnf_transformation,[],[f1875]) ).

fof(f2457,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X0)),X1))
          | X0 = one_one_nat )
        & ( one_one_nat != X0
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X0)),X1)) ) ) ),
    inference(nnf_transformation,[],[f1876]) ).

fof(f2458,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f919]) ).

fof(f2459,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
        | X0 != X1 ) ),
    inference(flattening,[],[f2458]) ).

fof(f2467,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
        | X0 = X1 ) ),
    inference(nnf_transformation,[],[f950]) ).

fof(f2468,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
        | X0 = X1 ) ),
    inference(flattening,[],[f2467]) ).

fof(f2469,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X0),X2)
        | X1 = X2 )
      & ( X1 != X2
        | hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X0),X2) ) ),
    inference(nnf_transformation,[],[f956]) ).

fof(f2470,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X2),X1)
        | X0 = X2 )
      & ( X0 != X2
        | hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X2),X1) ) ),
    inference(nnf_transformation,[],[f957]) ).

fof(f2471,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( ( hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),X1)
          | X2 = X0 )
        & ( X0 != X2
          | hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f1950]) ).

fof(f2472,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ) ),
    inference(nnf_transformation,[],[f1954]) ).

fof(f2473,plain,
    ! [X0] :
      ( ( zero_zero_nat = X0
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | X0 != zero_zero_nat ) ),
    inference(nnf_transformation,[],[f982]) ).

fof(f2474,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
    inference(nnf_transformation,[],[f985]) ).

fof(f2475,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat
        | ( X1 = zero_zero_nat
          & X0 = zero_zero_nat ) )
      & ( zero_zero_nat != X1
        | zero_zero_nat != X0
        | hAPP_nat_nat(plus_plus_nat(X0),X1) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f987]) ).

fof(f2476,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat
        | ( X1 = zero_zero_nat
          & X0 = zero_zero_nat ) )
      & ( zero_zero_nat != X1
        | zero_zero_nat != X0
        | hAPP_nat_nat(plus_plus_nat(X0),X1) = zero_zero_nat ) ),
    inference(flattening,[],[f2475]) ).

fof(f2477,plain,
    ! [X0] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
        | X0 = zero_zero_nat )
      & ( zero_zero_nat != X0
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
    inference(nnf_transformation,[],[f991]) ).

fof(f2478,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X0),X1)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f994]) ).

fof(f2479,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != zero_zero_nat
        | X1 = zero_zero_nat
        | X0 = zero_zero_nat )
      & ( ( zero_zero_nat != X1
          & zero_zero_nat != X0 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f997]) ).

fof(f2480,plain,
    ! [X0,X1] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != zero_zero_nat
        | X1 = zero_zero_nat
        | X0 = zero_zero_nat )
      & ( ( zero_zero_nat != X1
          & zero_zero_nat != X0 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(flattening,[],[f2479]) ).

fof(f2483,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X2),X1)
        | X1 = zero_zero_nat
        | X0 = X2 )
      & ( ( zero_zero_nat != X1
          & X0 != X2 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X2),X1) ) ),
    inference(nnf_transformation,[],[f999]) ).

fof(f2484,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X2),X1)
        | X1 = zero_zero_nat
        | X0 = X2 )
      & ( ( zero_zero_nat != X1
          & X0 != X2 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X2),X1) ) ),
    inference(flattening,[],[f2483]) ).

fof(f2485,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ) ),
    inference(nnf_transformation,[],[f1002]) ).

fof(f2486,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(nnf_transformation,[],[f1010]) ).

fof(f2487,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( X0 != X1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) )
      & ( X0 = X1
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1011]) ).

fof(f2488,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( X0 != X1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) )
      & ( X0 = X1
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(flattening,[],[f2487]) ).

fof(f2491,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ) ),
    inference(nnf_transformation,[],[f1975]) ).

fof(f2492,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))) ) ),
    inference(nnf_transformation,[],[f1018]) ).

fof(f2493,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ? [X2] : X1 = hAPP_nat_nat(plus_plus_nat(X0),X2) )
      & ( ! [X2] : hAPP_nat_nat(plus_plus_nat(X0),X2) != X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1023]) ).

fof(f2494,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ? [X3] : hAPP_nat_nat(plus_plus_nat(X0),X3) = X1 )
      & ( ! [X2] : hAPP_nat_nat(plus_plus_nat(X0),X2) != X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(rectify,[],[f2493]) ).

fof(f2495,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,X1)) = X1 )
      & ( ! [X2] : hAPP_nat_nat(plus_plus_nat(X0),X2) != X1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1))],[f2494]) ).

fof(f2496,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ) ),
    inference(nnf_transformation,[],[f1024]) ).

fof(f2497,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1))) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f1033]) ).

fof(f2498,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f1994]) ).

fof(f2503,plain,
    ! [X0,X1] :
      ( ( one_one_nat != hAPP_nat_nat(times_times_nat(X0),X1)
        | ( X1 = one_one_nat
          & X0 = one_one_nat ) )
      & ( one_one_nat != X1
        | one_one_nat != X0
        | one_one_nat = hAPP_nat_nat(times_times_nat(X0),X1) ) ),
    inference(nnf_transformation,[],[f1053]) ).

fof(f2504,plain,
    ! [X0,X1] :
      ( ( one_one_nat != hAPP_nat_nat(times_times_nat(X0),X1)
        | ( X1 = one_one_nat
          & X0 = one_one_nat ) )
      & ( one_one_nat != X1
        | one_one_nat != X0
        | one_one_nat = hAPP_nat_nat(times_times_nat(X0),X1) ) ),
    inference(flattening,[],[f2503]) ).

fof(f2505,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1))) ) ),
    inference(nnf_transformation,[],[f1056]) ).

fof(f2506,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1))) ) ),
    inference(flattening,[],[f2505]) ).

fof(f2507,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X3] :
              ( hAPP_nat_nat(plus_plus_nat(X2),X3) != X1
              | hBOOL(hAPP_nat_bool(X0,X3)) )
          & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
            | hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) )
      & ( ? [X3] :
            ( hAPP_nat_nat(plus_plus_nat(X2),X3) = X1
            & ~ hBOOL(hAPP_nat_bool(X0,X3)) )
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(nnf_transformation,[],[f2006]) ).

fof(f2508,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X3] :
              ( hAPP_nat_nat(plus_plus_nat(X2),X3) != X1
              | hBOOL(hAPP_nat_bool(X0,X3)) )
          & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
            | hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) )
      & ( ? [X3] :
            ( hAPP_nat_nat(plus_plus_nat(X2),X3) = X1
            & ~ hBOOL(hAPP_nat_bool(X0,X3)) )
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(flattening,[],[f2507]) ).

fof(f2509,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X4] :
              ( hAPP_nat_nat(plus_plus_nat(X2),X4) != X1
              | hBOOL(hAPP_nat_bool(X0,X4)) )
          & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
            | hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) )
      & ( ? [X3] :
            ( hAPP_nat_nat(plus_plus_nat(X2),X3) = X1
            & ~ hBOOL(hAPP_nat_bool(X0,X3)) )
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(rectify,[],[f2508]) ).

fof(f2510,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X4] :
              ( hAPP_nat_nat(plus_plus_nat(X2),X4) != X1
              | hBOOL(hAPP_nat_bool(X0,X4)) )
          & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
            | hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) )
      & ( ( hAPP_nat_nat(plus_plus_nat(X2),sK19(X0,X1,X2)) = X1
          & ~ hBOOL(hAPP_nat_bool(X0,sK19(X0,X1,X2))) )
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1,X2))],[f2509]) ).

fof(f2511,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X3] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | hAPP_nat_nat(plus_plus_nat(X2),X3) != X1 )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) )
      & ( ? [X3] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & hAPP_nat_nat(plus_plus_nat(X2),X3) = X1 )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(nnf_transformation,[],[f2007]) ).

fof(f2512,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X3] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | hAPP_nat_nat(plus_plus_nat(X2),X3) != X1 )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) )
      & ( ? [X3] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & hAPP_nat_nat(plus_plus_nat(X2),X3) = X1 )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(flattening,[],[f2511]) ).

fof(f2513,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X4] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | hAPP_nat_nat(plus_plus_nat(X2),X4) != X1 )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) )
      & ( ? [X3] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & hAPP_nat_nat(plus_plus_nat(X2),X3) = X1 )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(rectify,[],[f2512]) ).

fof(f2514,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
        | ( ! [X4] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | hAPP_nat_nat(plus_plus_nat(X2),X4) != X1 )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) )
      & ( ( ~ hBOOL(hAPP_nat_bool(X0,sK20(X0,X1,X2)))
          & hAPP_nat_nat(plus_plus_nat(X2),sK20(X0,X1,X2)) = X1 )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f2513]) ).

fof(f2515,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(nnf_transformation,[],[f1061]) ).

fof(f2516,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(flattening,[],[f2515]) ).

fof(f2517,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(nnf_transformation,[],[f1062]) ).

fof(f2518,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(flattening,[],[f2517]) ).

fof(f2519,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) ) ),
    inference(nnf_transformation,[],[f1063]) ).

fof(f2520,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
        | ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) ) ),
    inference(flattening,[],[f2519]) ).

fof(f2521,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(nnf_transformation,[],[f2018]) ).

fof(f2522,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(flattening,[],[f2521]) ).

fof(f2523,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(nnf_transformation,[],[f2019]) ).

fof(f2524,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ),
    inference(flattening,[],[f2523]) ).

fof(f2525,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(sK21(X0,X1)),one_one_nat)))
        & ! [X3] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK21(X0,X1)))
            | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK21(X0,X1)),X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X2,sK21(X0,X1))],[f2021]) ).

fof(f2526,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2))) ) ) ),
    inference(nnf_transformation,[],[f2022]) ).

fof(f2527,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X0),X2)
        | X1 = X2
        | X0 = zero_zero_nat )
      & ( ( X1 != X2
          & zero_zero_nat != X0 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),X2) ) ),
    inference(nnf_transformation,[],[f1071]) ).

fof(f2528,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X0),X2)
        | X1 = X2
        | X0 = zero_zero_nat )
      & ( ( X1 != X2
          & zero_zero_nat != X0 )
        | hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),X2) ) ),
    inference(flattening,[],[f2527]) ).

fof(f2530,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f2024]) ).

fof(f2531,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
        | X0 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
          & zero_zero_nat != X0 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(nnf_transformation,[],[f1075]) ).

fof(f2532,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
        | X0 = zero_zero_nat )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
          & zero_zero_nat != X0 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ) ),
    inference(flattening,[],[f2531]) ).

fof(f2533,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f2025]) ).

fof(f2534,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1))) ) ) ),
    inference(nnf_transformation,[],[f2026]) ).

fof(f2535,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2))) ) ) ),
    inference(nnf_transformation,[],[f2027]) ).

fof(f2536,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)
          | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1) = X2 )
        & ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1) != X2
          | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2) ) ) ),
    inference(nnf_transformation,[],[f2029]) ).

fof(f2537,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2))) ) ) ),
    inference(nnf_transformation,[],[f2030]) ).

fof(f2538,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)
          | X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) )
        & ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) != X1
          | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2) ) ) ),
    inference(nnf_transformation,[],[f2032]) ).

fof(f2539,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2))) ) ) ),
    inference(nnf_transformation,[],[f2033]) ).

fof(f2540,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
          | ? [X1,X2] :
              ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) = X0
              & is_int(X2)
              & is_int(X1) ) )
        & ( ! [X1,X2] :
              ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) != X0
              | ~ is_int(X2)
              | ~ is_int(X1) )
          | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ) ) ),
    inference(nnf_transformation,[],[f2035]) ).

fof(f2541,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
          | ? [X3,X4] :
              ( twoSqu1241645765sum2sq(product_Pair_int_int(X3,X4)) = X0
              & is_int(X4)
              & is_int(X3) ) )
        & ( ! [X1,X2] :
              ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) != X0
              | ~ is_int(X2)
              | ~ is_int(X1) )
          | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ) ) ),
    inference(rectify,[],[f2540]) ).

fof(f2542,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ( ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
          | ( twoSqu1241645765sum2sq(product_Pair_int_int(sK22(X0),sK23(X0))) = X0
            & is_int(sK23(X0))
            & is_int(sK22(X0)) ) )
        & ( ! [X1,X2] :
              ( twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) != X0
              | ~ is_int(X2)
              | ~ is_int(X1) )
          | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X3,sK22(X0)),skolemize(X4,sK23(X0))],[f2541]) ).

fof(f2553,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | zero_zero_int = X2
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) )
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
          | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ) ) ),
    inference(nnf_transformation,[],[f2039]) ).

fof(f2554,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X4] :
          ( is_int(X4)
          & hBOOL(hAPP_int_bool(X1,X4))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X4),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X3] :
          ( ~ hBOOL(hAPP_int_bool(X1,X3))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(rectify,[],[f2041]) ).

fof(f2555,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( is_int(sK24(X1,X2))
        & hBOOL(hAPP_int_bool(X1,sK24(X1,X2)))
        & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(sK24(X1,X2)),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X3] :
          ( ~ hBOOL(hAPP_int_bool(X1,X3))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X4,sK24(X1,X2))],[f2554]) ).

fof(f2556,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ? [X4] :
          ( is_int(X4)
          & hBOOL(hAPP_int_bool(X1,X4))
          & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X4),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X3] :
          ( ~ hBOOL(hAPP_int_bool(X1,X3))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(rectify,[],[f2043]) ).

fof(f2557,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( is_int(sK25(X1,X2))
        & hBOOL(hAPP_int_bool(X1,sK25(X1,X2)))
        & ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(sK25(X1,X2)),X2))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ! [X3] :
          ( ~ hBOOL(hAPP_int_bool(X1,X3))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X4,sK25(X1,X2))],[f2556]) ).

fof(f2558,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(X0)),X0))
        & hBOOL(hAPP_int_bool(zprime,sK26(X0)))
        & is_int(sK26(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X1,sK26(X0))],[f2044]) ).

fof(f2559,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ( ! [X3] :
            ( ~ is_int(X3)
            | ~ hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
            | sK27(X0,X1) = X3 )
        & hBOOL(hAPP_int_bool(zcong(X0,sK27(X0,X1)),X1))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,X1)),X1))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK27(X0,X1)))
        & is_int(sK27(X0,X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X2,sK27(X0,X1))],[f2046]) ).

fof(f2560,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ( is_int(sK28(X0,X2))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK28(X0,X2)),X2))
        & hBOOL(hAPP_int_bool(X0,sK28(X0,X2)))
        & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK28(X0,X2)),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X3,sK28(X0,X2))],[f2112]) ).

fof(f2561,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ( is_int(sK29(X0,X2))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK29(X0,X2)),X2))
        & hBOOL(hAPP_int_bool(X0,sK29(X0,X2)))
        & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK29(X0,X2)),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X3,sK29(X0,X2))],[f2114]) ).

fof(f2562,plain,
    ! [X0,X1] :
      ( ( is_int(sK30(X1))
        & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),sK30(X1)))
          | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(sK30(X1)),one_one_int))) )
        & ~ hBOOL(hAPP_int_bool(X1,sK30(X1))) )
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X2,sK30(X1))],[f2116]) ).

fof(f2563,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ( is_int(sK31(X0,X1))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK31(X0,X1)))
        & hBOOL(hAPP_int_bool(X0,sK31(X0,X1)))
        & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK31(X0,X1)),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X3,sK31(X0,X1))],[f2118]) ).

fof(f2564,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ( is_int(sK32(X0,X1))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sK32(X0,X1)))
        & hBOOL(hAPP_int_bool(X0,sK32(X0,X1)))
        & ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK32(X0,X1)),one_one_int))) )
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(X3,sK32(X0,X1))],[f2120]) ).

fof(f2565,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK33(X2)),sK34(X2)))
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X2,sK33(X2))),hAPP_nat_nat(X2,sK34(X2)))) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X2,X0)),X1)),hAPP_nat_nat(X2,hAPP_nat_nat(plus_plus_nat(X0),X1)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34]),skolemize(X3,sK33(X2)),skolemize(X4,sK34(X2))],[f2121]) ).

fof(f2566,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ( hBOOL(hAPP_nat_bool(X1,sK35(X0,X1)))
        & ! [X3] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK35(X0,X1)))
            | ~ hBOOL(hAPP_nat_bool(X1,X3)) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK35(X0,X1)),X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(X2,sK35(X0,X1))],[f2124]) ).

fof(f2567,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,X1)) = X1
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK36(X0,X1))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(X2,sK36(X0,X1))],[f2130]) ).

fof(f2570,plain,
    ! [X0] :
      ( ( zero_zero_nat = X0
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat))
        | X0 != zero_zero_nat ) ),
    inference(nnf_transformation,[],[f1146]) ).

fof(f2571,plain,
    ! [X0] :
      ( ( zero_zero_nat = X0
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat))
        | X0 != zero_zero_nat ) ),
    inference(flattening,[],[f2570]) ).

fof(f2575,plain,
    ! [X0,X1,X2] :
      ( zero_zero_nat = X2
      | ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2))) ) ) ),
    inference(nnf_transformation,[],[f2138]) ).

fof(f2576,plain,
    ! [X0,X1] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1)))
        | hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)) = zero_zero_int )
      & ( zero_zero_int != hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1))) ) ),
    inference(nnf_transformation,[],[f1162]) ).

fof(f2577,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
          | ? [X2] :
              ( X0 = hAPP_int_int(times_times_int(X1),X2)
              & is_int(X2) ) )
        & ( ! [X2] :
              ( hAPP_int_int(times_times_int(X1),X2) != X0
              | ~ is_int(X2) )
          | hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int ) ) ),
    inference(nnf_transformation,[],[f2152]) ).

fof(f2578,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
          | ? [X3] :
              ( hAPP_int_int(times_times_int(X1),X3) = X0
              & is_int(X3) ) )
        & ( ! [X2] :
              ( hAPP_int_int(times_times_int(X1),X2) != X0
              | ~ is_int(X2) )
          | hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int ) ) ),
    inference(rectify,[],[f2577]) ).

fof(f2579,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ( ( zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
          | ( hAPP_int_int(times_times_int(X1),sK37(X0,X1)) = X0
            & is_int(sK37(X0,X1)) ) )
        & ( ! [X2] :
              ( hAPP_int_int(times_times_int(X1),X2) != X0
              | ~ is_int(X2) )
          | hAPP_int_int(div_mod_int(X0),X1) = zero_zero_int ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(X3,sK37(X0,X1))],[f2578]) ).

fof(f2580,plain,
    ! [X0,X1,X2] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1)
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2))) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2)))
        | hAPP_int_int(div_mod_int(X0),X1) = hAPP_int_int(div_mod_int(X2),X1) ) ),
    inference(nnf_transformation,[],[f1168]) ).

fof(f2581,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
        | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2)) )
      & ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2))
        | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
    inference(nnf_transformation,[],[f1171]) ).

fof(f2583,plain,
    ! [X0,X2,X1] :
      ( ( ~ sP3(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
        | ! [X3,X4] :
            ( ~ is_int(X4)
            | ~ is_int(X3)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
            | hBOOL(hAPP_int_bool(X0,X4)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
          & ? [X3,X4] :
              ( is_int(X4)
              & is_int(X3)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) = X1
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
              & ~ hBOOL(hAPP_int_bool(X0,X4)) ) )
        | sP3(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f2209]) ).

fof(f2584,plain,
    ! [X0,X2,X1] :
      ( ( ~ sP3(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
        | ! [X3,X4] :
            ( ~ is_int(X4)
            | ~ is_int(X3)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
            | hBOOL(hAPP_int_bool(X0,X4)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
          & ? [X3,X4] :
              ( is_int(X4)
              & is_int(X3)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) = X1
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
              & ~ hBOOL(hAPP_int_bool(X0,X4)) ) )
        | sP3(X0,X2,X1) ) ),
    inference(flattening,[],[f2583]) ).

fof(f2585,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP3(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
          & ? [X3,X4] :
              ( is_int(X4)
              & is_int(X3)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),X4) = X2
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X1))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
              & ~ hBOOL(hAPP_int_bool(X0,X4)) ) )
        | sP3(X0,X1,X2) ) ),
    inference(rectify,[],[f2584]) ).

fof(f2586,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP3(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
          & is_int(sK39(X0,X1,X2))
          & is_int(sK38(X0,X1,X2))
          & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),sK38(X0,X1,X2))),sK39(X0,X1,X2)) = X2
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK39(X0,X1,X2)),X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK39(X0,X1,X2)))
          & ~ hBOOL(hAPP_int_bool(X0,sK39(X0,X1,X2))) )
        | sP3(X0,X1,X2) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39]),skolemize(X3,sK38(X0,X1,X2)),skolemize(X4,sK39(X0,X1,X2))],[f2585]) ).

fof(f2591,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ( ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
          | ( sP2(X0,X2,X1)
            & sP3(X0,X2,X1)
            & ( zero_zero_int != X2
              | hBOOL(hAPP_int_bool(X0,X1)) ) ) )
        & ( ~ sP2(X0,X2,X1)
          | ~ sP3(X0,X2,X1)
          | ( zero_zero_int = X2
            & ~ hBOOL(hAPP_int_bool(X0,X1)) )
          | hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ) ) ),
    inference(nnf_transformation,[],[f2210]) ).

fof(f2592,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ( ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
          | ( sP2(X0,X2,X1)
            & sP3(X0,X2,X1)
            & ( zero_zero_int != X2
              | hBOOL(hAPP_int_bool(X0,X1)) ) ) )
        & ( ~ sP2(X0,X2,X1)
          | ~ sP3(X0,X2,X1)
          | ( zero_zero_int = X2
            & ~ hBOOL(hAPP_int_bool(X0,X1)) )
          | hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ) ) ),
    inference(flattening,[],[f2591]) ).

fof(f2593,plain,
    ! [X0] :
      ( ( zero_zero_int = hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls))))
        | hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) = one_one_int )
      & ( one_one_int != hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls))))
        | hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int ) ),
    inference(nnf_transformation,[],[f1198]) ).

fof(f2594,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | ( hAPP_int_int(times_times_int(X1),sK42(X0,X1)) = X0
        & is_int(sK42(X0,X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(X2,sK42(X0,X1))],[f2186]) ).

fof(f2595,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(div_mod_nat(X0),X1)
        | ? [X2] : X0 = hAPP_nat_nat(times_times_nat(X1),X2) )
      & ( ! [X2] : hAPP_nat_nat(times_times_nat(X1),X2) != X0
        | hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat ) ),
    inference(nnf_transformation,[],[f1205]) ).

fof(f2596,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(div_mod_nat(X0),X1)
        | ? [X3] : hAPP_nat_nat(times_times_nat(X1),X3) = X0 )
      & ( ! [X2] : hAPP_nat_nat(times_times_nat(X1),X2) != X0
        | hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat ) ),
    inference(rectify,[],[f2595]) ).

fof(f2597,plain,
    ! [X0,X1] :
      ( ( zero_zero_nat != hAPP_nat_nat(div_mod_nat(X0),X1)
        | hAPP_nat_nat(times_times_nat(X1),sK43(X0,X1)) = X0 )
      & ( ! [X2] : hAPP_nat_nat(times_times_nat(X1),X2) != X0
        | hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(X3,sK43(X0,X1))],[f2596]) ).

fof(f2599,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
        | standardRes(X1,X0) != zero_zero_int )
      & ( zero_zero_int = standardRes(X1,X0)
        | ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ) ),
    inference(nnf_transformation,[],[f1216]) ).

fof(f2604,plain,
    ! [X0,X1,X2] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
        | sP4(X1,X0,X2) )
      & ( ~ sP4(X1,X0,X2)
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2))) ) ),
    inference(nnf_transformation,[],[f2212]) ).

fof(f2605,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ( ( standardRes(X2,X0) != standardRes(X2,X1)
          | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) )
        & ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
          | standardRes(X2,X0) = standardRes(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f2202]) ).

fof(f2606,plain,
    is_int(one_one_int),
    inference(cnf_transformation,[],[f1]) ).

fof(f2608,plain,
    is_int(undefined_int(int)),
    inference(cnf_transformation,[],[f3]) ).

fof(f2609,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(multInv(X0,X1)) ),
    inference(cnf_transformation,[],[f1236]) ).

fof(f2610,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | is_int(zfact(X0)) ),
    inference(cnf_transformation,[],[f1237]) ).

fof(f2613,plain,
    is_int(min),
    inference(cnf_transformation,[],[f8]) ).

fof(f2614,plain,
    is_int(pls),
    inference(cnf_transformation,[],[f9]) ).

fof(f2615,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | is_int(number_number_of_int(X0)) ),
    inference(cnf_transformation,[],[f1240]) ).

fof(f2616,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(legendre(X0,X1)) ),
    inference(cnf_transformation,[],[f1242]) ).

fof(f2618,plain,
    ! [X0] : is_int(twoSqu1241645765sum2sq(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f2619,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | is_int(inv(X0,X1)) ),
    inference(cnf_transformation,[],[f1246]) ).

fof(f2622,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | is_int(hAPP_int_int(X0,X1)) ),
    inference(cnf_transformation,[],[f1249]) ).

fof(f2624,plain,
    ! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
    inference(cnf_transformation,[],[f19]) ).

fof(f2627,plain,
    is_int(m),
    inference(cnf_transformation,[],[f22]) ).

fof(f2628,plain,
    is_int(s1),
    inference(cnf_transformation,[],[f23]) ).

fof(f2629,plain,
    is_int(s),
    inference(cnf_transformation,[],[f24]) ).

fof(f2630,plain,
    is_int(t),
    inference(cnf_transformation,[],[f25]) ).

fof(f2631,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    inference(cnf_transformation,[],[f26]) ).

fof(f2632,plain,
    ( one_one_int != t
    | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(bit0(bit1(pls))))) ),
    inference(cnf_transformation,[],[f2213]) ).

fof(f2635,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(bit0(bit1(pls))))) ),
    inference(cnf_transformation,[],[f2214]) ).

fof(f2638,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f29]) ).

fof(f2639,plain,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f30]) ).

fof(f2640,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
    inference(cnf_transformation,[],[f31]) ).

fof(f2641,plain,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t))),
    inference(cnf_transformation,[],[f32]) ).

fof(f2643,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit1(bit1(pls))))),
    inference(cnf_transformation,[],[f34]) ).

fof(f2644,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1)),
    inference(cnf_transformation,[],[f35]) ).

fof(f2645,plain,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1)),
    inference(cnf_transformation,[],[f36]) ).

fof(f2646,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),X1)),
    inference(cnf_transformation,[],[f37]) ).

fof(f2650,plain,
    ! [X0] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f41]) ).

fof(f2654,plain,
    ! [X0] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(X0),X0),
    inference(cnf_transformation,[],[f45]) ).

fof(f2655,plain,
    ! [X0] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(X0),X0),
    inference(cnf_transformation,[],[f46]) ).

fof(f2656,plain,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(X0),X0),
    inference(cnf_transformation,[],[f47]) ).

fof(f2660,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X1)),
    inference(cnf_transformation,[],[f51]) ).

fof(f2661,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X1)),
    inference(cnf_transformation,[],[f52]) ).

fof(f2662,plain,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X1)),
    inference(cnf_transformation,[],[f53]) ).

fof(f2663,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X0)),
    inference(cnf_transformation,[],[f54]) ).

fof(f2664,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X0)),
    inference(cnf_transformation,[],[f55]) ).

fof(f2665,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),bit1(pls))),
    inference(cnf_transformation,[],[f56]) ).

fof(f2666,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),bit1(pls))),
    inference(cnf_transformation,[],[f57]) ).

fof(f2669,plain,
    is_int(sK9),
    inference(cnf_transformation,[],[f2215]) ).

fof(f2670,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),sK9),
    inference(cnf_transformation,[],[f2215]) ).

fof(f2671,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
    inference(cnf_transformation,[],[f61]) ).

fof(f2672,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f2677,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ),
    inference(cnf_transformation,[],[f1259]) ).

fof(f2678,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1261]) ).

fof(f2679,plain,
    ! [X2,X0,X1] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f67]) ).

fof(f2680,plain,
    ! [X2,X0,X1] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f68]) ).

fof(f2681,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f69]) ).

fof(f2688,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0))) ),
    inference(cnf_transformation,[],[f2219]) ).

fof(f2689,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2219]) ).

fof(f2690,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f2220]) ).

fof(f2691,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2220]) ).

fof(f2694,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2222]) ).

fof(f2695,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2222]) ).

fof(f2698,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2224]) ).

fof(f2699,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2224]) ).

fof(f2700,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X3),X1))) ),
    inference(cnf_transformation,[],[f1264]) ).

fof(f2701,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f82]) ).

fof(f2702,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f83]) ).

fof(f2703,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f84]) ).

fof(f2706,plain,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),X0) = hAPP_nat_nat(times_times_nat(X0),number_number_of_nat(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f87]) ).

fof(f2707,plain,
    number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
    inference(cnf_transformation,[],[f88]) ).

fof(f2710,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit1(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2226]) ).

fof(f2711,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit1(X1))) ),
    inference(cnf_transformation,[],[f2226]) ).

fof(f2714,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit1(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2228]) ).

fof(f2715,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit1(X1))) ),
    inference(cnf_transformation,[],[f2228]) ).

fof(f2719,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit0(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2230]) ).

fof(f2720,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit0(X1))) ),
    inference(cnf_transformation,[],[f2230]) ).

fof(f2724,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit0(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2232]) ).

fof(f2725,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit0(X1))) ),
    inference(cnf_transformation,[],[f2232]) ).

fof(f2726,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2233]) ).

fof(f2727,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2233]) ).

fof(f2728,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2234]) ).

fof(f2729,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2234]) ).

fof(f2730,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X0)),hAPP_int_int(plus_plus_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1265]) ).

fof(f2731,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1266]) ).

fof(f2732,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) ),
    inference(cnf_transformation,[],[f1267]) ).

fof(f2733,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | number_number_of_nat(X1) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1267]) ).

fof(f2734,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | number_number_of_nat(X0) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1267]) ).

fof(f2735,plain,
    one_one_nat = number_number_of_nat(bit1(pls)),
    inference(cnf_transformation,[],[f104]) ).

fof(f2737,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2235]) ).

fof(f2738,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ),
    inference(cnf_transformation,[],[f2235]) ).

fof(f2739,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2236]) ).

fof(f2740,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ),
    inference(cnf_transformation,[],[f2236]) ).

fof(f2743,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit0(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2238]) ).

fof(f2744,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),bit0(X1))) ),
    inference(cnf_transformation,[],[f2238]) ).

fof(f2747,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit1(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2240]) ).

fof(f2748,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),bit1(X1))) ),
    inference(cnf_transformation,[],[f2240]) ).

fof(f2750,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2241]) ).

fof(f2751,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1)) ),
    inference(cnf_transformation,[],[f2241]) ).

fof(f2752,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2242]) ).

fof(f2753,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f2242]) ).

fof(f2754,plain,
    hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f115]) ).

fof(f2755,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1270]) ).

fof(f2768,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f129]) ).

fof(f2769,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f130]) ).

fof(f2770,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    inference(cnf_transformation,[],[f131]) ).

fof(f2774,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)),
    inference(cnf_transformation,[],[f135]) ).

fof(f2775,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(cnf_transformation,[],[f136]) ).

fof(f2776,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X2)),
    inference(cnf_transformation,[],[f137]) ).

fof(f2777,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(X1),X0) = hAPP_int_int(times_times_int(X0),X1),
    inference(cnf_transformation,[],[f138]) ).

fof(f2778,plain,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    inference(cnf_transformation,[],[f139]) ).

fof(f2779,plain,
    ! [X0,X1] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    inference(cnf_transformation,[],[f140]) ).

fof(f2783,plain,
    ! [X0,X1] :
      ( ~ hBOOL(member_int(X0,X1))
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f2243]) ).

fof(f2784,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(X1,X0))
      | hBOOL(member_int(X0,X1)) ),
    inference(cnf_transformation,[],[f2243]) ).

fof(f2785,plain,
    ! [X0] : collect_int(X0) = X0,
    inference(cnf_transformation,[],[f145]) ).

fof(f2789,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f149]) ).

fof(f2790,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f150]) ).

fof(f2791,plain,
    ! [X2,X0,X1] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    inference(cnf_transformation,[],[f151]) ).

fof(f2794,plain,
    ! [X2,X0,X1] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    inference(cnf_transformation,[],[f154]) ).

fof(f2795,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    inference(cnf_transformation,[],[f155]) ).

fof(f2797,plain,
    ! [X2,X0,X1] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X2)),
    inference(cnf_transformation,[],[f157]) ).

fof(f2798,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    inference(cnf_transformation,[],[f158]) ).

fof(f2799,plain,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(cnf_transformation,[],[f159]) ).

fof(f2800,plain,
    ! [X0,X1] : hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0),
    inference(cnf_transformation,[],[f160]) ).

fof(f2801,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | number_number_of_int(X0) != number_number_of_int(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2244]) ).

fof(f2803,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | number267125858f_real(X0) != number267125858f_real(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2245]) ).

fof(f2811,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | bit1(X0) != bit1(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2249]) ).

fof(f2813,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | bit0(X0) != bit0(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2250]) ).

fof(f2815,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f168]) ).

fof(f2816,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(X1),X0) = hAPP_int_int(times_times_int(X0),X1),
    inference(cnf_transformation,[],[f169]) ).

fof(f2817,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | number_number_of_int(X0) = X0 ),
    inference(cnf_transformation,[],[f1280]) ).

fof(f2818,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f171]) ).

fof(f2819,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    inference(cnf_transformation,[],[f172]) ).

fof(f2820,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    inference(cnf_transformation,[],[f173]) ).

fof(f2825,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit0(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2253]) ).

fof(f2826,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),bit0(X1))) ),
    inference(cnf_transformation,[],[f2253]) ).

fof(f2829,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2255]) ).

fof(f2830,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X0))) ),
    inference(cnf_transformation,[],[f2255]) ).

fof(f2831,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2256]) ).

fof(f2832,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ),
    inference(cnf_transformation,[],[f2256]) ).

fof(f2835,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit1(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2258]) ).

fof(f2836,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),bit1(X1))) ),
    inference(cnf_transformation,[],[f2258]) ).

fof(f2837,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2259]) ).

fof(f2838,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),pls)) ),
    inference(cnf_transformation,[],[f2259]) ).

fof(f2839,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2260]) ).

fof(f2840,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X0))) ),
    inference(cnf_transformation,[],[f2260]) ).

fof(f2844,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f185]) ).

fof(f2845,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f186]) ).

fof(f2846,plain,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),number_number_of_nat(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f187]) ).

fof(f2847,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) ),
    inference(cnf_transformation,[],[f2263]) ).

fof(f2848,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f2263]) ).

fof(f2849,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls))) ),
    inference(cnf_transformation,[],[f2264]) ).

fof(f2850,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),bit1(pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(cnf_transformation,[],[f2264]) ).

fof(f2851,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) ),
    inference(cnf_transformation,[],[f2265]) ).

fof(f2852,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2265]) ).

fof(f2853,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0)) ),
    inference(cnf_transformation,[],[f2266]) ).

fof(f2854,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f2266]) ).

fof(f2855,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) ),
    inference(cnf_transformation,[],[f2267]) ).

fof(f2856,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f2267]) ).

fof(f2857,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls))) ),
    inference(cnf_transformation,[],[f2268]) ).

fof(f2858,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),bit1(pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(cnf_transformation,[],[f2268]) ).

fof(f2859,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) ),
    inference(cnf_transformation,[],[f2269]) ).

fof(f2860,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2269]) ).

fof(f2861,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0)) ),
    inference(cnf_transformation,[],[f2270]) ).

fof(f2862,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f2270]) ).

fof(f2878,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | X0 = X1
      | X2 = X3
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X3),X0)) ),
    inference(cnf_transformation,[],[f2278]) ).

fof(f2881,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | X2 = X3
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),hAPP_nat_nat(times_times_nat(X3),X0)) ),
    inference(cnf_transformation,[],[f2280]) ).

fof(f2884,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | X2 = X3
      | hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X3),X0)) ),
    inference(cnf_transformation,[],[f2282]) ).

fof(f2887,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    inference(cnf_transformation,[],[f208]) ).

fof(f2889,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)),
    inference(cnf_transformation,[],[f210]) ).

fof(f2892,plain,
    ! [X0] : hAPP_real_real(times_times_real(X0),one_one_real) = X0,
    inference(cnf_transformation,[],[f213]) ).

fof(f2899,plain,
    ! [X0] : bit1(X0) != pls,
    inference(cnf_transformation,[],[f220]) ).

fof(f2901,plain,
    ! [X0,X1] : bit1(X0) != bit0(X1),
    inference(cnf_transformation,[],[f222]) ).

fof(f2907,plain,
    pls = bit0(pls),
    inference(cnf_transformation,[],[f226]) ).

fof(f2913,plain,
    ! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(cnf_transformation,[],[f232]) ).

fof(f2914,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(X0),one_one_int) = X0 ),
    inference(cnf_transformation,[],[f1293]) ).

fof(f2915,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(one_one_int),X0) = X0 ),
    inference(cnf_transformation,[],[f1294]) ).

fof(f2916,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),
    inference(cnf_transformation,[],[f235]) ).

fof(f2918,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    inference(cnf_transformation,[],[f237]) ).

fof(f2919,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f238]) ).

fof(f2921,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) ),
    inference(cnf_transformation,[],[f1298]) ).

fof(f2924,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) ),
    inference(cnf_transformation,[],[f1304]) ).

fof(f2926,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),
    inference(cnf_transformation,[],[f245]) ).

fof(f2936,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0),
    inference(cnf_transformation,[],[f255]) ).

fof(f2937,plain,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X0)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)),X0),
    inference(cnf_transformation,[],[f256]) ).

fof(f2938,plain,
    ! [X0,X1] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),X0),
    inference(cnf_transformation,[],[f257]) ).

fof(f2939,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0),
    inference(cnf_transformation,[],[f258]) ).

fof(f2940,plain,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),X0) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0),
    inference(cnf_transformation,[],[f259]) ).

fof(f2941,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(X0),X0) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0),
    inference(cnf_transformation,[],[f260]) ).

fof(f2946,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),X2)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f265]) ).

fof(f2947,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(number267125858f_real(X1)),X2)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f266]) ).

fof(f2950,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),
    inference(cnf_transformation,[],[f269]) ).

fof(f2951,plain,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(times_times_int(X0),X1)) = hAPP_real_real(times_times_real(number267125858f_real(X0)),number267125858f_real(X1)),
    inference(cnf_transformation,[],[f270]) ).

fof(f2952,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f271]) ).

fof(f2953,plain,
    ! [X2,X0,X1] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(plus_plus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f272]) ).

fof(f2955,plain,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)),
    inference(cnf_transformation,[],[f274]) ).

fof(f2956,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f275]) ).

fof(f2957,plain,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)),
    inference(cnf_transformation,[],[f276]) ).

fof(f2959,plain,
    ! [X0,X1] : bit1(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(bit0(X0)),bit1(X1)),
    inference(cnf_transformation,[],[f278]) ).

fof(f2960,plain,
    ! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
    inference(cnf_transformation,[],[f279]) ).

fof(f2961,plain,
    ! [X0] : number_number_of_int(bit1(X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X0)),
    inference(cnf_transformation,[],[f280]) ).

fof(f2962,plain,
    ! [X0] : number267125858f_real(bit1(X0)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0))),number267125858f_real(X0)),
    inference(cnf_transformation,[],[f281]) ).

fof(f2967,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(cnf_transformation,[],[f286]) ).

fof(f2969,plain,
    one_one_real = number267125858f_real(bit1(pls)),
    inference(cnf_transformation,[],[f288]) ).

fof(f2975,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(bit1(X0)),X1) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(X0),X1))),X1),
    inference(cnf_transformation,[],[f294]) ).

fof(f2976,plain,
    ! [X0] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(bit0(X0)),
    inference(cnf_transformation,[],[f295]) ).

fof(f2977,plain,
    ! [X0] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) = number267125858f_real(bit0(X0)),
    inference(cnf_transformation,[],[f296]) ).

fof(f2978,plain,
    ! [X0] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),X0),
    inference(cnf_transformation,[],[f297]) ).

fof(f2979,plain,
    ! [X0] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),X0),
    inference(cnf_transformation,[],[f298]) ).

fof(f2980,plain,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X0)),X0),
    inference(cnf_transformation,[],[f299]) ).

fof(f2981,plain,
    ! [X0] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f300]) ).

fof(f2987,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),number_number_of_int(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f306]) ).

fof(f2989,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(X0),X0) = hAPP_real_real(times_times_real(X0),number267125858f_real(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f308]) ).

fof(f2995,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f314]) ).

fof(f2996,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int))),
    inference(cnf_transformation,[],[f315]) ).

fof(f2997,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | number_number_of_int(bit0(bit1(pls))) = X0
      | number_number_of_int(bit1(bit1(pls))) = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X0)) ),
    inference(cnf_transformation,[],[f1312]) ).

fof(f2998,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(cnf_transformation,[],[f317]) ).

fof(f3000,plain,
    ! [X0] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),number_number_of_nat(bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f319]) ).

fof(f3001,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    inference(cnf_transformation,[],[f1313]) ).

fof(f3002,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    inference(cnf_transformation,[],[f1314]) ).

fof(f3003,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    inference(cnf_transformation,[],[f1315]) ).

fof(f3004,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),X0)))) ),
    inference(cnf_transformation,[],[f1316]) ).

fof(f3005,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0)))) ),
    inference(cnf_transformation,[],[f1317]) ).

fof(f3006,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0)))) ),
    inference(cnf_transformation,[],[f1318]) ).

fof(f3010,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2285]) ).

fof(f3011,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1))) ),
    inference(cnf_transformation,[],[f2285]) ).

fof(f3012,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2286]) ).

fof(f3013,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2286]) ).

fof(f3014,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2287]) ).

fof(f3015,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1))) ),
    inference(cnf_transformation,[],[f2287]) ).

fof(f3016,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(s1),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f332]) ).

fof(f3017,plain,
    hBOOL(hAPP_int_bool(zcong(s1,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f333]) ).

fof(f3018,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f333]) ).

fof(f3019,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)),
    inference(cnf_transformation,[],[f333]) ).

fof(f3020,plain,
    ! [X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | sK10 = X1 ),
    inference(cnf_transformation,[],[f2288]) ).

fof(f3021,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f2288]) ).

fof(f3022,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f2288]) ).

fof(f3023,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK10)),
    inference(cnf_transformation,[],[f2288]) ).

fof(f3024,plain,
    is_int(sK10),
    inference(cnf_transformation,[],[f2288]) ).

fof(f3025,plain,
    is_int(sK11),
    inference(cnf_transformation,[],[f2289]) ).

fof(f3026,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f2289]) ).

fof(f3027,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f2289]) ).

fof(f3028,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK11)),
    inference(cnf_transformation,[],[f2289]) ).

fof(f3029,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s1),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f336]) ).

fof(f3039,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1333]) ).

fof(f3040,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1334]) ).

fof(f3041,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1335]) ).

fof(f3042,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X3),X1))) ),
    inference(cnf_transformation,[],[f1337]) ).

fof(f3043,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X3),X1))) ),
    inference(cnf_transformation,[],[f1339]) ).

fof(f3044,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X3),X1))) ),
    inference(cnf_transformation,[],[f1341]) ).

fof(f3045,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),X3)) ),
    inference(cnf_transformation,[],[f1343]) ).

fof(f3046,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),X3)) ),
    inference(cnf_transformation,[],[f1345]) ).

fof(f3047,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),X3)) ),
    inference(cnf_transformation,[],[f1347]) ).

fof(f3048,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X2),X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(cnf_transformation,[],[f1349]) ).

fof(f3049,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(cnf_transformation,[],[f1351]) ).

fof(f3050,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),X1) != hAPP_nat_real(power_power_real(X2),X1)
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(cnf_transformation,[],[f1353]) ).

fof(f3051,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1355]) ).

fof(f3052,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1357]) ).

fof(f3054,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1360]) ).

fof(f3055,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1361]) ).

fof(f3057,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | zero_zero_int = X1
      | zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) ),
    inference(cnf_transformation,[],[f1364]) ).

fof(f3058,plain,
    ! [X0,X1] :
      ( zero_zero_real = X1
      | hAPP_nat_real(power_power_real(X1),X0) != zero_zero_real ),
    inference(cnf_transformation,[],[f1365]) ).

fof(f3059,plain,
    ! [X0] :
      ( zero_zero_nat = X0
      | zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) ),
    inference(cnf_transformation,[],[f1366]) ).

fof(f3063,plain,
    ! [X0] :
      ( zero_zero_nat = X0
      | zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) ),
    inference(cnf_transformation,[],[f1368]) ).

fof(f3066,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1372]) ).

fof(f3067,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1374]) ).

fof(f3068,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1376]) ).

fof(f3077,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0,
    inference(cnf_transformation,[],[f375]) ).

fof(f3081,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),X1) != X0
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f2296]) ).

fof(f3085,plain,
    ! [X0,X1] :
      ( hAPP_real_real(plus_plus_real(X0),X1) != X0
      | zero_zero_real = X1 ),
    inference(cnf_transformation,[],[f2298]) ).

fof(f3086,plain,
    ! [X0,X1] :
      ( zero_zero_real != X1
      | hAPP_real_real(plus_plus_real(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f2298]) ).

fof(f3087,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(plus_plus_int(X0),X0)
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2299]) ).

fof(f3089,plain,
    ! [X0] :
      ( hAPP_real_real(plus_plus_real(X0),X0) != zero_zero_real
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2300]) ).

fof(f3091,plain,
    zero_zero_int = pls,
    inference(cnf_transformation,[],[f384]) ).

fof(f3093,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
    inference(cnf_transformation,[],[f1382]) ).

fof(f3094,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),zero_zero_int) = X0 ),
    inference(cnf_transformation,[],[f1383]) ).

fof(f3097,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1386]) ).

fof(f3098,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1388]) ).

fof(f3099,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1390]) ).

fof(f3100,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X0)),hAPP_nat_real(power_power_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1392]) ).

fof(f3101,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1393]) ).

fof(f3103,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1395]) ).

fof(f3104,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X2),one_one_int),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),X0)),one_one_int),X3)) ),
    inference(cnf_transformation,[],[f1396]) ).

fof(f3105,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2301]) ).

fof(f3106,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2301]) ).

fof(f3107,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2))) ),
    inference(cnf_transformation,[],[f2302]) ).

fof(f3108,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X4))),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(plus_plus_int(X1),X2))) ),
    inference(cnf_transformation,[],[f2302]) ).

fof(f3109,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(cnf_transformation,[],[f1399]) ).

fof(f3110,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f1401]) ).

fof(f3111,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ),
    inference(cnf_transformation,[],[f1403]) ).

fof(f3112,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(cnf_transformation,[],[f1405]) ).

fof(f3113,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f1407]) ).

fof(f3114,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(cnf_transformation,[],[f1409]) ).

fof(f3115,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(cnf_transformation,[],[f1411]) ).

fof(f3116,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f1413]) ).

fof(f3117,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(cnf_transformation,[],[f1415]) ).

fof(f3120,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2304]) ).

fof(f3121,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2304]) ).

fof(f3122,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f2306]) ).

fof(f3123,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2306]) ).

fof(f3128,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ is_int(X4)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X4
      | X0 = X1
      | X2 != X3
      | hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(X4),X0)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) ),
    inference(cnf_transformation,[],[f1419]) ).

fof(f3129,plain,
    ! [X2,X3,X0,X1,X4] :
      ( zero_zero_nat = X4
      | X0 = X1
      | X2 != X3
      | hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X4),X0)) != hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X1)) ),
    inference(cnf_transformation,[],[f1421]) ).

fof(f3130,plain,
    ! [X2,X3,X0,X1,X4] :
      ( zero_zero_real = X4
      | X0 = X1
      | X2 != X3
      | hAPP_real_real(plus_plus_real(X2),hAPP_real_real(times_times_real(X4),X0)) != hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X1)) ),
    inference(cnf_transformation,[],[f1423]) ).

fof(f3131,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_nat_int(power_power_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(cnf_transformation,[],[f1425]) ).

fof(f3132,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(cnf_transformation,[],[f417]) ).

fof(f3138,plain,
    number267125858f_real(pls) = zero_zero_real,
    inference(cnf_transformation,[],[f423]) ).

fof(f3141,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
    inference(cnf_transformation,[],[f425]) ).

fof(f3142,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2310]) ).

fof(f3143,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2310]) ).

fof(f3144,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(cnf_transformation,[],[f427]) ).

fof(f3145,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    inference(cnf_transformation,[],[f428]) ).

fof(f3146,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f1427]) ).

fof(f3150,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),X0))),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(cnf_transformation,[],[f1433]) ).

fof(f3151,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),X0))),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1435]) ).

fof(f3152,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(cnf_transformation,[],[f1437]) ).

fof(f3153,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),hAPP_int_int(times_times_int(X1),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X3),X0)),X1)) ),
    inference(cnf_transformation,[],[f1439]) ).

fof(f3154,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(cnf_transformation,[],[f437]) ).

fof(f3155,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))),
    inference(cnf_transformation,[],[f438]) ).

fof(f3156,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f2312]) ).

fof(f3157,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2312]) ).

fof(f3159,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real))
      | zero_zero_real = X1 ),
    inference(cnf_transformation,[],[f2314]) ).

fof(f3160,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2314]) ).

fof(f3162,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f3163,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f3165,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2316]) ).

fof(f3166,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)),
    inference(cnf_transformation,[],[f442]) ).

fof(f3167,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    inference(cnf_transformation,[],[f443]) ).

fof(f3169,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(cnf_transformation,[],[f2318]) ).

fof(f3170,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(cnf_transformation,[],[f2318]) ).

fof(f3172,plain,
    ! [X0,X1] :
      ( zero_zero_real = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))) ),
    inference(cnf_transformation,[],[f2320]) ).

fof(f3173,plain,
    ! [X0,X1] :
      ( zero_zero_real = X0
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))) ),
    inference(cnf_transformation,[],[f2320]) ).

fof(f3174,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2322]) ).

fof(f3175,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2322]) ).

fof(f3176,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2322]) ).

fof(f3177,plain,
    ! [X0] : number_number_of_int(bit0(X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X0))),number_number_of_int(X0)),
    inference(cnf_transformation,[],[f447]) ).

fof(f3179,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
    inference(cnf_transformation,[],[f1446]) ).

fof(f3180,plain,
    ! [X0] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f450]) ).

fof(f3181,plain,
    ! [X0] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f451]) ).

fof(f3182,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2323]) ).

fof(f3183,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f2323]) ).

fof(f3184,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | one_one_int != hAPP_int_int(times_times_int(X1),X0)
      | one_one_int = X0 ),
    inference(cnf_transformation,[],[f2325]) ).

fof(f3185,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | one_one_int != hAPP_int_int(times_times_int(X1),X0)
      | one_one_int = X1 ),
    inference(cnf_transformation,[],[f2325]) ).

fof(f3187,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2326]) ).

fof(f3188,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2326]) ).

fof(f3189,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2327]) ).

fof(f3190,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2327]) ).

fof(f3191,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2328]) ).

fof(f3192,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f2328]) ).

fof(f3193,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2329]) ).

fof(f3194,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2329]) ).

fof(f3195,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2330]) ).

fof(f3196,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2330]) ).

fof(f3197,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2331]) ).

fof(f3198,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f2331]) ).

fof(f3199,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2332]) ).

fof(f3200,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2332]) ).

fof(f3201,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2333]) ).

fof(f3202,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2333]) ).

fof(f3203,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2334]) ).

fof(f3204,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2334]) ).

fof(f3205,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X0))) ),
    inference(cnf_transformation,[],[f1449]) ).

fof(f3213,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))))),
    inference(cnf_transformation,[],[f469]) ).

fof(f3214,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),
    inference(cnf_transformation,[],[f470]) ).

fof(f3215,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f1452]) ).

fof(f3216,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1454]) ).

fof(f3217,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1456]) ).

fof(f3218,plain,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1458]) ).

fof(f3219,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1460]) ).

fof(f3220,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1462]) ).

fof(f3221,plain,
    ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
    inference(cnf_transformation,[],[f477]) ).

fof(f3222,plain,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
    inference(cnf_transformation,[],[f478]) ).

fof(f3224,plain,
    ! [X0] :
      ( zero_zero_real = X0
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))))) ),
    inference(cnf_transformation,[],[f2337]) ).

fof(f3226,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | zero_zero_int = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))) ),
    inference(cnf_transformation,[],[f2338]) ).

fof(f3230,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f2342]) ).

fof(f3231,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2342]) ).

fof(f3236,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)),
    inference(cnf_transformation,[],[f486]) ).

fof(f3237,plain,
    ! [X2,X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X1),X2)),
    inference(cnf_transformation,[],[f487]) ).

fof(f3238,plain,
    ! [X2,X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X2)),
    inference(cnf_transformation,[],[f488]) ).

fof(f3239,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f489]) ).

fof(f3240,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f490]) ).

fof(f3241,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f491]) ).

fof(f3242,plain,
    ! [X0] : one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0),
    inference(cnf_transformation,[],[f492]) ).

fof(f3244,plain,
    ! [X0] : one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0),
    inference(cnf_transformation,[],[f494]) ).

fof(f3245,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f495]) ).

fof(f3246,plain,
    ! [X2,X0,X1] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f496]) ).

fof(f3247,plain,
    ! [X2,X0,X1] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f497]) ).

fof(f3251,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))),
    inference(cnf_transformation,[],[f501]) ).

fof(f3252,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),
    inference(cnf_transformation,[],[f502]) ).

fof(f3253,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
      | zero_zero_real = X1 ),
    inference(cnf_transformation,[],[f2344]) ).

fof(f3254,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2344]) ).

fof(f3256,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f2346]) ).

fof(f3257,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2346]) ).

fof(f3259,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
    inference(cnf_transformation,[],[f505]) ).

fof(f3260,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
    inference(cnf_transformation,[],[f506]) ).

fof(f3262,plain,
    ! [X0,X1] :
      ( zero_zero_real = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
    inference(cnf_transformation,[],[f2348]) ).

fof(f3263,plain,
    ! [X0,X1] :
      ( zero_zero_real = X0
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
    inference(cnf_transformation,[],[f2348]) ).

fof(f3265,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
    inference(cnf_transformation,[],[f2350]) ).

fof(f3266,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
    inference(cnf_transformation,[],[f2350]) ).

fof(f3267,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)))),
    inference(cnf_transformation,[],[f509]) ).

fof(f3268,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1)))),
    inference(cnf_transformation,[],[f510]) ).

fof(f3269,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1476]) ).

fof(f3270,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(cnf_transformation,[],[f1477]) ).

fof(f3271,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1478]) ).

fof(f3272,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1480]) ).

fof(f3273,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1482]) ).

fof(f3274,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1484]) ).

fof(f3275,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | hAPP_nat_real(power_power_real(X2),X0) != hAPP_nat_real(power_power_real(X2),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2351]) ).

fof(f3277,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | hAPP_nat_nat(power_power_nat(X2),X0) != hAPP_nat_nat(power_power_nat(X2),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2352]) ).

fof(f3279,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | hAPP_nat_int(power_power_int(X2),X0) != hAPP_nat_int(power_power_int(X2),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2353]) ).

fof(f3287,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1492]) ).

fof(f3288,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1494]) ).

fof(f3289,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1496]) ).

fof(f3290,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1498]) ).

fof(f3291,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1500]) ).

fof(f3292,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1502]) ).

fof(f3293,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f529]) ).

fof(f3294,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(cnf_transformation,[],[f1504]) ).

fof(f3295,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(bit0(bit1(pls)))))
      | one_one_int = X0
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f1506]) ).

fof(f3296,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_real))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f1507]) ).

fof(f3297,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X1))),zero_zero_int))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f1509]) ).

fof(f3298,plain,
    ! [X2,X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | X0 = X2
      | one_one_int = X2 ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3299,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3300,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | is_int(sK12(X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3301,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK12(X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3302,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK12(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3303,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | sK12(X0) != X0
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3304,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | one_one_int != sK12(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3305,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int)) ),
    inference(cnf_transformation,[],[f1513]) ).

fof(f3306,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
    inference(cnf_transformation,[],[f1515]) ).

fof(f3307,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f537]) ).

fof(f3308,plain,
    is_int(sK13),
    inference(cnf_transformation,[],[f2361]) ).

fof(f3309,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK13),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f2361]) ).

fof(f3310,plain,
    one_one_int = legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),
    inference(cnf_transformation,[],[f539]) ).

fof(f3312,plain,
    ! [X0,X1] :
      ( zero_zero_nat != X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f2363]) ).

fof(f3314,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | zero_zero_nat = X1 ),
    inference(cnf_transformation,[],[f2365]) ).

fof(f3315,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f2365]) ).

fof(f3319,plain,
    ! [X0,X1] :
      ( number_number_of_nat(X1) != zero_zero_nat
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)))) ),
    inference(cnf_transformation,[],[f2367]) ).

fof(f3320,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1518]) ).

fof(f3321,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | bit1(X0) != min
      | min = X0 ),
    inference(cnf_transformation,[],[f2368]) ).

fof(f3322,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | min != X0
      | bit1(X0) = min ),
    inference(cnf_transformation,[],[f2368]) ).

fof(f3325,plain,
    min = bit1(min),
    inference(cnf_transformation,[],[f546]) ).

fof(f3327,plain,
    min != pls,
    inference(cnf_transformation,[],[f548]) ).

fof(f3329,plain,
    ! [X0] : bit0(X0) != min,
    inference(cnf_transformation,[],[f550]) ).

fof(f3330,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
    inference(cnf_transformation,[],[f551]) ).

fof(f3332,plain,
    ! [X0] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2370]) ).

fof(f3334,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(cnf_transformation,[],[f2371]) ).

fof(f3335,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),min)) ),
    inference(cnf_transformation,[],[f2371]) ).

fof(f3336,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f2372]) ).

fof(f3337,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(X0))) ),
    inference(cnf_transformation,[],[f2372]) ).

fof(f3338,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
    inference(cnf_transformation,[],[f556]) ).

fof(f3340,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f2373]) ).

fof(f3341,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(X0))) ),
    inference(cnf_transformation,[],[f2373]) ).

fof(f3342,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
    inference(cnf_transformation,[],[f559]) ).

fof(f3343,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f2374]) ).

fof(f3344,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),min)) ),
    inference(cnf_transformation,[],[f2374]) ).

fof(f3345,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(cnf_transformation,[],[f2375]) ).

fof(f3346,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(X0))) ),
    inference(cnf_transformation,[],[f2375]) ).

fof(f3347,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
    inference(cnf_transformation,[],[f562]) ).

fof(f3348,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
    inference(cnf_transformation,[],[f563]) ).

fof(f3349,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f2376]) ).

fof(f3350,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X0)),min)) ),
    inference(cnf_transformation,[],[f2376]) ).

fof(f3351,plain,
    number_number_of_int(pls) != number_number_of_int(min),
    inference(cnf_transformation,[],[f565]) ).

fof(f3352,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f1522]) ).

fof(f3354,plain,
    ! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat),
    inference(cnf_transformation,[],[f568]) ).

fof(f3356,plain,
    ! [X0] : one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat),
    inference(cnf_transformation,[],[f570]) ).

fof(f3358,plain,
    ! [X0] : one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat),
    inference(cnf_transformation,[],[f572]) ).

fof(f3360,plain,
    zero_zero_nat = number_number_of_nat(pls),
    inference(cnf_transformation,[],[f574]) ).

fof(f3361,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f2377]) ).

fof(f3362,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(X0))) ),
    inference(cnf_transformation,[],[f2377]) ).

fof(f3363,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f2378]) ).

fof(f3364,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X0)),min)) ),
    inference(cnf_transformation,[],[f2378]) ).

fof(f3365,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | number_number_of_int(min) = X0
      | one_one_int = X0 ),
    inference(cnf_transformation,[],[f1524]) ).

fof(f3366,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | number_number_of_int(min) = X1
      | one_one_int = X1 ),
    inference(cnf_transformation,[],[f2380]) ).

fof(f3367,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | number_number_of_int(min) = X0
      | one_one_int = X1 ),
    inference(cnf_transformation,[],[f2380]) ).

fof(f3368,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | one_one_int != hAPP_int_int(times_times_int(X0),X1)
      | number_number_of_int(min) = X1
      | one_one_int = X0 ),
    inference(cnf_transformation,[],[f2380]) ).

fof(f3372,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1528]) ).

fof(f3373,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X0))) ),
    inference(cnf_transformation,[],[f1530]) ).

fof(f3374,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1532]) ).

fof(f3376,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(cnf_transformation,[],[f1533]) ).

fof(f3378,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3380,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(cnf_transformation,[],[f1535]) ).

fof(f3381,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2381]) ).

fof(f3382,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(cnf_transformation,[],[f2381]) ).

fof(f3385,plain,
    ! [X0] :
      ( number_number_of_nat(X0) != zero_zero_nat
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2383]) ).

fof(f3386,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | number_number_of_nat(X0) = zero_zero_nat ),
    inference(cnf_transformation,[],[f2383]) ).

fof(f3387,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    inference(cnf_transformation,[],[f2384]) ).

fof(f3389,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
    inference(cnf_transformation,[],[f589]) ).

fof(f3391,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f591]) ).

fof(f3392,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(X2),X0))),X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f3393,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
      | zero_zero_nat = hAPP_nat_nat(times_times_nat(number_number_of_nat(X2)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),X1)) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f3394,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) ),
    inference(cnf_transformation,[],[f1539]) ).

fof(f3395,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = zero_zero_nat ),
    inference(cnf_transformation,[],[f1539]) ).

fof(f3401,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2385]) ).

fof(f3403,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
    inference(cnf_transformation,[],[f600]) ).

fof(f3404,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),X0),hAPP_int_int(times_times_int(X3),X1)),X4)) ),
    inference(cnf_transformation,[],[f1551]) ).

fof(f3405,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X0),X2)),X3)) ),
    inference(cnf_transformation,[],[f1552]) ).

fof(f3406,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),hAPP_int_int(times_times_int(X2),X0)),X3)) ),
    inference(cnf_transformation,[],[f1553]) ).

fof(f3407,plain,
    ! [X2,X0,X1] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),X1)),X1)),
    inference(cnf_transformation,[],[f604]) ).

fof(f3408,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X2),X0),hAPP_int_int(plus_plus_int(X3),X1)),X4)) ),
    inference(cnf_transformation,[],[f1555]) ).

fof(f3409,plain,
    ! [X0] : one_one_real = hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),
    inference(cnf_transformation,[],[f606]) ).

fof(f3410,plain,
    ! [X0] : one_one_int = hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),
    inference(cnf_transformation,[],[f607]) ).

fof(f3411,plain,
    ! [X0,X1] :
      ( zero_zero_real != hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1))
      | number_number_of_nat(X1) != zero_zero_nat ),
    inference(cnf_transformation,[],[f2387]) ).

fof(f3414,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1))
      | number_number_of_nat(X1) != zero_zero_nat ),
    inference(cnf_transformation,[],[f2389]) ).

fof(f3417,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1))
      | number_number_of_nat(X1) != zero_zero_nat ),
    inference(cnf_transformation,[],[f2391]) ).

fof(f3420,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    inference(cnf_transformation,[],[f611]) ).

fof(f3422,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1560]) ).

fof(f3423,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1)) ),
    inference(cnf_transformation,[],[f1562]) ).

fof(f3424,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1563]) ).

fof(f3425,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),sK14(X0,X1,X2))) = X1 ),
    inference(cnf_transformation,[],[f2394]) ).

fof(f3426,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | is_int(sK14(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f2394]) ).

fof(f3427,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3)) != X1
      | ~ is_int(X3)
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f2394]) ).

fof(f3428,plain,
    ! [X0] :
      ( number_number_of_nat(X0) = zero_zero_nat
      | zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1565]) ).

fof(f3429,plain,
    ! [X0] :
      ( number_number_of_nat(X0) != zero_zero_nat
      | one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1565]) ).

fof(f3430,plain,
    ! [X0] :
      ( number_number_of_nat(X0) = zero_zero_nat
      | zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1566]) ).

fof(f3431,plain,
    ! [X0] :
      ( number_number_of_nat(X0) != zero_zero_nat
      | one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1566]) ).

fof(f3432,plain,
    ! [X0] :
      ( number_number_of_nat(X0) = zero_zero_nat
      | zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1567]) ).

fof(f3433,plain,
    ! [X0] :
      ( number_number_of_nat(X0) != zero_zero_nat
      | one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X0)) ),
    inference(cnf_transformation,[],[f1567]) ).

fof(f3434,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1))
      | X0 = X2 ),
    inference(cnf_transformation,[],[f1569]) ).

fof(f3436,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    inference(cnf_transformation,[],[f622]) ).

fof(f3437,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
    inference(cnf_transformation,[],[f1573]) ).

fof(f3438,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ),
    inference(cnf_transformation,[],[f1575]) ).

fof(f3439,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4)) ),
    inference(cnf_transformation,[],[f1577]) ).

fof(f3440,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
    inference(cnf_transformation,[],[f1579]) ).

fof(f3441,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1581]) ).

fof(f3442,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f1583]) ).

fof(f3444,plain,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),number_number_of_int(min))),
    inference(cnf_transformation,[],[f630]) ).

fof(f3446,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2))
      | hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) ),
    inference(cnf_transformation,[],[f1587]) ).

fof(f3447,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,number_number_of_int(min)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(cnf_transformation,[],[f1589]) ).

fof(f3448,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0)) ),
    inference(cnf_transformation,[],[f1590]) ).

fof(f3449,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min)),
    inference(cnf_transformation,[],[f635]) ).

fof(f3450,plain,
    ( hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),number_number_of_int(min)))
    | one_one_int != legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)) ),
    inference(cnf_transformation,[],[f1591]) ).

fof(f3451,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X0)
      | hAPP_int_int(minus_minus_int(X0),X1) != X2
      | hAPP_int_int(plus_plus_int(X2),X1) = X0 ),
    inference(cnf_transformation,[],[f1593]) ).

fof(f3452,plain,
    ! [X0,X1] : number267125858f_real(hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_real_real(minus_minus_real(number267125858f_real(X0)),number267125858f_real(X1)),
    inference(cnf_transformation,[],[f638]) ).

fof(f3453,plain,
    ! [X0,X1] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),number_number_of_int(X1)),
    inference(cnf_transformation,[],[f639]) ).

fof(f3454,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(minus_minus_int(X0),pls) = X0 ),
    inference(cnf_transformation,[],[f1594]) ).

fof(f3456,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),X2)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)),
    inference(cnf_transformation,[],[f642]) ).

fof(f3457,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),X1)),X2) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f643]) ).

fof(f3458,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X4))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X2),X0),hAPP_int_int(minus_minus_int(X3),X1)),X4)) ),
    inference(cnf_transformation,[],[f1596]) ).

fof(f3459,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1598]) ).

fof(f3460,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(X1),X2)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(X0)),X1)),hAPP_real_real(times_times_real(number267125858f_real(X0)),X2)),
    inference(cnf_transformation,[],[f646]) ).

fof(f3462,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X0),X1)),number267125858f_real(X2)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X0),number267125858f_real(X2))),hAPP_real_real(times_times_real(X1),number267125858f_real(X2))),
    inference(cnf_transformation,[],[f648]) ).

fof(f3464,plain,
    ! [X0,X1] : hAPP_int_int(minus_minus_int(bit1(X0)),bit0(X1)) = bit1(hAPP_int_int(minus_minus_int(X0),X1)),
    inference(cnf_transformation,[],[f650]) ).

fof(f3465,plain,
    ! [X0,X1] : bit0(hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(bit1(X0)),bit1(X1)),
    inference(cnf_transformation,[],[f651]) ).

fof(f3466,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),bit0(X0)) = bit0(hAPP_int_int(minus_minus_int(pls),X0)),
    inference(cnf_transformation,[],[f652]) ).

fof(f3467,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2395]) ).

fof(f3468,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2395]) ).

fof(f3469,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X4),hAPP_int_int(times_times_int(X1),X5))),X6)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X4),X6))),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),hAPP_int_int(times_times_int(X5),X6)))),
    inference(cnf_transformation,[],[f654]) ).

fof(f3470,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1))) ),
    inference(cnf_transformation,[],[f2396]) ).

fof(f3471,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1)))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f2396]) ).

fof(f3472,plain,
    ! [X2,X0,X1] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f656]) ).

fof(f3473,plain,
    ! [X2,X0,X1] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f657]) ).

fof(f3474,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(cnf_transformation,[],[f1600]) ).

fof(f3476,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f2397]) ).

fof(f3477,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),bit1(X0)) = bit1(hAPP_int_int(minus_minus_int(min),X0)),
    inference(cnf_transformation,[],[f660]) ).

fof(f3478,plain,
    ! [X0] : bit1(hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),bit0(X0)),
    inference(cnf_transformation,[],[f661]) ).

fof(f3479,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(min),bit1(X0)) = bit0(hAPP_int_int(minus_minus_int(min),X0)),
    inference(cnf_transformation,[],[f662]) ).

fof(f3480,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1)) ),
    inference(cnf_transformation,[],[f2398]) ).

fof(f3481,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f2398]) ).

fof(f3482,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | X1 != X3
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X4))
      | hBOOL(hAPP_int_bool(zcong(X2,X0),X4)) ),
    inference(cnf_transformation,[],[f1602]) ).

fof(f3483,plain,
    ! [X2,X3,X0,X1] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))),twoSqu1241645765sum2sq(product_Pair_int_int(X2,X3))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X1),X2)))),
    inference(cnf_transformation,[],[f665]) ).

fof(f3484,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(cnf_transformation,[],[f1604]) ).

fof(f3485,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hAPP_int_int(minus_minus_int(X1),one_one_int) = X0
      | one_one_int = X0 ),
    inference(cnf_transformation,[],[f1606]) ).

fof(f3486,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f668]) ).

fof(f3487,plain,
    ! [X0] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
    inference(cnf_transformation,[],[f669]) ).

fof(f3488,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4)) ),
    inference(cnf_transformation,[],[f2399]) ).

fof(f3489,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X3),X1)),X4))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X2),X1)),X4)) ),
    inference(cnf_transformation,[],[f2399]) ).

fof(f3490,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4)) ),
    inference(cnf_transformation,[],[f2400]) ).

fof(f3491,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X3)),X4))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X4)) ),
    inference(cnf_transformation,[],[f2400]) ).

fof(f3492,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X1),X0),hAPP_int_int(plus_plus_int(X2),X0)),X3)) ),
    inference(cnf_transformation,[],[f1609]) ).

fof(f3493,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X0),hAPP_nat_int(power_power_int(X2),X0)),X3)) ),
    inference(cnf_transformation,[],[f1610]) ).

fof(f3494,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X0)),X1)),
    inference(cnf_transformation,[],[f674]) ).

fof(f3495,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1)),
    inference(cnf_transformation,[],[f675]) ).

fof(f3496,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0)),X1))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f676]) ).

fof(f3497,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit1(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit1(bit1(pls))))),
    inference(cnf_transformation,[],[f677]) ).

fof(f3498,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | X1 = X2 ),
    inference(cnf_transformation,[],[f1612]) ).

fof(f3499,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f1614]) ).

fof(f3500,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1616]) ).

fof(f3503,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    inference(cnf_transformation,[],[f2402]) ).

fof(f3504,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2402]) ).

fof(f3505,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(cnf_transformation,[],[f1618]) ).

fof(f3506,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X0))
      | zero_zero_int = X1 ),
    inference(cnf_transformation,[],[f1620]) ).

fof(f3507,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2))) ),
    inference(cnf_transformation,[],[f1622]) ).

fof(f3508,plain,
    ! [X0] :
      ( number_number_of_int(min) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X0)
      | one_one_int = hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) ),
    inference(cnf_transformation,[],[f686]) ).

fof(f3509,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),zero_zero_int),X2)) ),
    inference(cnf_transformation,[],[f1624]) ).

fof(f3513,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)))
      | one_one_int = legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f1631]) ).

fof(f3514,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(quadRes(X1),X0))
      | legendre(X0,X1) = number_number_of_int(min) ),
    inference(cnf_transformation,[],[f1632]) ).

fof(f3515,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(quadRes(X1),X0))
      | one_one_int = legendre(X0,X1) ),
    inference(cnf_transformation,[],[f1632]) ).

fof(f3516,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | zero_zero_int = legendre(X0,X1) ),
    inference(cnf_transformation,[],[f1632]) ).

fof(f3517,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),X0)),X1))
      | X0 = X1
      | zero_zero_nat = X1 ),
    inference(cnf_transformation,[],[f1634]) ).

fof(f3518,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),number_number_of_nat(bit0(bit1(pls)))),X1),X0)) ),
    inference(cnf_transformation,[],[f2405]) ).

fof(f3519,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
      | is_int(sK15(X0,X1)) ),
    inference(cnf_transformation,[],[f2405]) ).

fof(f3520,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
      | ~ is_int(X2)
      | hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(cnf_transformation,[],[f2405]) ).

fof(f3521,plain,
    ! [X0,X1] :
      ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
      | zero_zero_real = X1 ),
    inference(cnf_transformation,[],[f2407]) ).

fof(f3522,plain,
    ! [X0,X1] :
      ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2407]) ).

fof(f3524,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | one_one_real != hAPP_real_real(plus_plus_real(X1),X0)
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X3)),hAPP_real_real(times_times_real(X0),X2))),X4)) ),
    inference(cnf_transformation,[],[f1636]) ).

fof(f3525,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | one_one_int != hAPP_int_int(plus_plus_int(X1),X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(times_times_int(X0),X2))),X4)) ),
    inference(cnf_transformation,[],[f1638]) ).

fof(f3526,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),zero_zero_real)),
    inference(cnf_transformation,[],[f698]) ).

fof(f3528,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),zero_zero_int)),
    inference(cnf_transformation,[],[f700]) ).

fof(f3529,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2408]) ).

fof(f3530,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2408]) ).

fof(f3531,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ),
    inference(cnf_transformation,[],[f1640]) ).

fof(f3533,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X0)),
    inference(cnf_transformation,[],[f704]) ).

fof(f3535,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X0)),
    inference(cnf_transformation,[],[f706]) ).

fof(f3536,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0)) ),
    inference(cnf_transformation,[],[f1644]) ).

fof(f3538,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    inference(cnf_transformation,[],[f1648]) ).

fof(f3543,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f2412]) ).

fof(f3544,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2412]) ).

fof(f3545,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2412]) ).

fof(f3549,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    inference(cnf_transformation,[],[f714]) ).

fof(f3550,plain,
    ! [X0,X1] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    inference(cnf_transformation,[],[f715]) ).

fof(f3551,plain,
    ! [X0] : hAPP_real_real(times_times_real(one_one_real),X0) = X0,
    inference(cnf_transformation,[],[f716]) ).

fof(f3552,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1649]) ).

fof(f3553,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_nat_nat(power_power_nat(X0),X1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) ),
    inference(cnf_transformation,[],[f1650]) ).

fof(f3554,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_nat_real(power_power_real(X0),X1) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) ),
    inference(cnf_transformation,[],[f1651]) ).

fof(f3555,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hAPP_nat_int(power_power_int(X0),X1) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))),X0) ),
    inference(cnf_transformation,[],[f1652]) ).

fof(f3556,plain,
    ! [X0,X1] :
      ( zero_zero_nat = X1
      | hAPP_nat_nat(times_times_nat(X1),X0) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),one_one_nat)),X0)) ),
    inference(cnf_transformation,[],[f1653]) ).

fof(f3558,plain,
    ! [X0,X1] :
      ( zero_zero_nat = X1
      | hAPP_nat_nat(power_power_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))) ),
    inference(cnf_transformation,[],[f1654]) ).

fof(f3560,plain,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)),
    inference(cnf_transformation,[],[f723]) ).

fof(f3567,plain,
    ! [X0,X1] :
      ( hAPP_real_real(times_times_real(X0),X1) != zero_zero_real
      | zero_zero_real = X1
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2416]) ).

fof(f3570,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(times_times_int(X0),X1)
      | zero_zero_int = X1
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f2418]) ).

fof(f3573,plain,
    ! [X0] : zero_zero_real = hAPP_real_real(times_times_real(X0),zero_zero_real),
    inference(cnf_transformation,[],[f732]) ).

fof(f3575,plain,
    ! [X0] : zero_zero_int = hAPP_int_int(times_times_int(X0),zero_zero_int),
    inference(cnf_transformation,[],[f734]) ).

fof(f3576,plain,
    ! [X0] : zero_zero_real = hAPP_real_real(times_times_real(zero_zero_real),X0),
    inference(cnf_transformation,[],[f735]) ).

fof(f3578,plain,
    ! [X0] : zero_zero_int = hAPP_int_int(times_times_int(zero_zero_int),X0),
    inference(cnf_transformation,[],[f737]) ).

fof(f3582,plain,
    one_one_real != zero_zero_real,
    inference(cnf_transformation,[],[f741]) ).

fof(f3583,plain,
    one_one_nat != zero_zero_nat,
    inference(cnf_transformation,[],[f742]) ).

fof(f3584,plain,
    one_one_int != zero_zero_int,
    inference(cnf_transformation,[],[f743]) ).

fof(f3585,plain,
    ! [X2,X3,X0,X1] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f744]) ).

fof(f3586,plain,
    ! [X2,X3,X0,X1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f745]) ).

fof(f3587,plain,
    ! [X2,X3,X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f746]) ).

fof(f3590,plain,
    ! [X2,X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f749]) ).

fof(f3591,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f1669]) ).

fof(f3593,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),X0))
      | zero_zero_int = X0 ),
    inference(cnf_transformation,[],[f1672]) ).

fof(f3594,plain,
    ! [X2,X3,X0,X1] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(X0),X2)),hAPP_real_real(minus_minus_real(X1),X3)),
    inference(cnf_transformation,[],[f753]) ).

fof(f3595,plain,
    ! [X2,X3,X0,X1] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X2)),hAPP_int_int(minus_minus_int(X1),X3)),
    inference(cnf_transformation,[],[f754]) ).

fof(f3596,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2)) ),
    inference(cnf_transformation,[],[f1673]) ).

fof(f3597,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f1674]) ).

fof(f3598,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2)) ),
    inference(cnf_transformation,[],[f1675]) ).

fof(f3599,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2)) ),
    inference(cnf_transformation,[],[f1676]) ).

fof(f3600,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f1677]) ).

fof(f3601,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    inference(cnf_transformation,[],[f1678]) ).

fof(f3605,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(cnf_transformation,[],[f1683]) ).

fof(f3606,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(cnf_transformation,[],[f1685]) ).

fof(f3607,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(cnf_transformation,[],[f1687]) ).

fof(f3608,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1688]) ).

fof(f3609,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1689]) ).

fof(f3610,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1690]) ).

fof(f3611,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1691]) ).

fof(f3612,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1692]) ).

fof(f3613,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1693]) ).

fof(f3614,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X0))),
    inference(cnf_transformation,[],[f773]) ).

fof(f3615,plain,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X0))),
    inference(cnf_transformation,[],[f774]) ).

fof(f3616,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X0))),
    inference(cnf_transformation,[],[f775]) ).

fof(f3617,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X0),X1))),
    inference(cnf_transformation,[],[f776]) ).

fof(f3618,plain,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X0),X1))),
    inference(cnf_transformation,[],[f777]) ).

fof(f3619,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X0),X1))),
    inference(cnf_transformation,[],[f778]) ).

fof(f3620,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(plus_plus_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1695]) ).

fof(f3621,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1697]) ).

fof(f3622,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(plus_plus_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1699]) ).

fof(f3623,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),X0)),
    inference(cnf_transformation,[],[f782]) ).

fof(f3625,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X0)),
    inference(cnf_transformation,[],[f784]) ).

fof(f3626,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(minus_minus_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1701]) ).

fof(f3627,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1703]) ).

fof(f3628,plain,
    ! [X2,X0,X1] :
      ( zero_zero_real = X2
      | hAPP_real_real(times_times_real(X0),X2) != hAPP_real_real(times_times_real(X1),X2)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2419]) ).

fof(f3630,plain,
    ! [X2,X0,X1] :
      ( zero_zero_real = X2
      | hAPP_real_real(times_times_real(X2),X1) != hAPP_real_real(times_times_real(X2),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2420]) ).

fof(f3632,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f1707]) ).

fof(f3638,plain,
    ! [X2,X0,X1] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)),
    inference(cnf_transformation,[],[f793]) ).

fof(f3639,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),X1) != zero_zero_nat
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2424]) ).

fof(f3641,plain,
    ! [X0,X1] :
      ( zero_zero_nat != X0
      | zero_zero_nat = X1
      | hAPP_nat_nat(power_power_nat(X0),X1) = zero_zero_nat ),
    inference(cnf_transformation,[],[f2424]) ).

fof(f3642,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X0)),hAPP_nat_nat(power_power_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1710]) ).

fof(f3645,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat)) ),
    inference(cnf_transformation,[],[f1712]) ).

fof(f3646,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat)) ),
    inference(cnf_transformation,[],[f1712]) ).

fof(f3647,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1713]) ).

fof(f3648,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1713]) ).

fof(f3653,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(cnf_transformation,[],[f1717]) ).

fof(f3655,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(cnf_transformation,[],[f1721]) ).

fof(f3656,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1))) ),
    inference(cnf_transformation,[],[f1723]) ).

fof(f3658,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(cnf_transformation,[],[f1727]) ).

fof(f3659,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f1729]) ).

fof(f3660,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f1731]) ).

fof(f3661,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1733]) ).

fof(f3662,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1735]) ).

fof(f3665,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f1741]) ).

fof(f3666,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f1743]) ).

fof(f3669,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X0)),hAPP_real_real(times_times_real(X2),X0))) ),
    inference(cnf_transformation,[],[f1749]) ).

fof(f3671,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(cnf_transformation,[],[f1753]) ).

fof(f3687,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f3688,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f3690,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f3691,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f3693,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2428]) ).

fof(f3694,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2428]) ).

fof(f3699,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
    inference(cnf_transformation,[],[f2430]) ).

fof(f3700,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f2430]) ).

fof(f3702,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f2430]) ).

fof(f3703,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f2430]) ).

fof(f3705,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2432]) ).

fof(f3706,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2432]) ).

fof(f3708,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f2432]) ).

fof(f3709,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f2432]) ).

fof(f3710,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0))),
    inference(cnf_transformation,[],[f838]) ).

fof(f3711,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X0))),
    inference(cnf_transformation,[],[f839]) ).

fof(f3725,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1809]) ).

fof(f3726,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1811]) ).

fof(f3729,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1817]) ).

fof(f3730,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0)) ),
    inference(cnf_transformation,[],[f2433]) ).

fof(f3732,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(cnf_transformation,[],[f2434]) ).

fof(f3734,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f1821]) ).

fof(f3736,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f1825]) ).

fof(f3737,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
    inference(cnf_transformation,[],[f1827]) ).

fof(f3740,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f1833]) ).

fof(f3743,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f1839]) ).

fof(f3745,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f1843]) ).

fof(f3748,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(cnf_transformation,[],[f1849]) ).

fof(f3749,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2435]) ).

fof(f3751,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2436]) ).

fof(f3753,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f3754,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f3755,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f3756,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f3757,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f2438]) ).

fof(f3759,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3760,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3761,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3762,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3763,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3764,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f2440]) ).

fof(f3765,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f3766,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2)) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f3767,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f3768,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f3769,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f2442]) ).

fof(f3771,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3772,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3773,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3774,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3775,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3776,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f2444]) ).

fof(f3777,plain,
    ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X0)),zero_zero_real)),
    inference(cnf_transformation,[],[f881]) ).

fof(f3778,plain,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X0)),zero_zero_int)),
    inference(cnf_transformation,[],[f882]) ).

fof(f3780,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1))) ),
    inference(cnf_transformation,[],[f1855]) ).

fof(f3782,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | zero_zero_nat = X1 ),
    inference(cnf_transformation,[],[f2446]) ).

fof(f3783,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2446]) ).

fof(f3785,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2447]) ).

fof(f3786,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2))) ),
    inference(cnf_transformation,[],[f2447]) ).

fof(f3787,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2448]) ).

fof(f3788,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2))) ),
    inference(cnf_transformation,[],[f2448]) ).

fof(f3789,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f2449]) ).

fof(f3790,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f2449]) ).

fof(f3791,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0))) ),
    inference(cnf_transformation,[],[f1862]) ).

fof(f3792,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f1864]) ).

fof(f3793,plain,
    ! [X0,X1] :
      ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))
      | zero_zero_real = X1 ),
    inference(cnf_transformation,[],[f2451]) ).

fof(f3794,plain,
    ! [X0,X1] :
      ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))
      | zero_zero_real = X0 ),
    inference(cnf_transformation,[],[f2451]) ).

fof(f3796,plain,
    ! [X2,X0,X1] :
      ( zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1866]) ).

fof(f3798,plain,
    ! [X0,X1] :
      ( one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1)
      | zero_zero_nat = X1
      | one_one_nat = X0 ),
    inference(cnf_transformation,[],[f2453]) ).

fof(f3799,plain,
    ! [X0,X1] :
      ( zero_zero_nat != X1
      | one_one_nat = hAPP_nat_nat(power_power_nat(X0),X1) ),
    inference(cnf_transformation,[],[f2453]) ).

fof(f3800,plain,
    ! [X0,X1] :
      ( one_one_nat != X0
      | one_one_nat = hAPP_nat_nat(power_power_nat(X0),X1) ),
    inference(cnf_transformation,[],[f2453]) ).

fof(f3801,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0)) ),
    inference(cnf_transformation,[],[f1870]) ).

fof(f3802,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X0))),
    inference(cnf_transformation,[],[f897]) ).

fof(f3803,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hAPP_nat_real(power_power_real(sK16(X0,X1)),X1) = X0 ),
    inference(cnf_transformation,[],[f2454]) ).

fof(f3804,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK16(X0,X1))) ),
    inference(cnf_transformation,[],[f2454]) ).

fof(f3805,plain,
    ! [X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hAPP_nat_real(power_power_real(X3),X1) != X0
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
      | sK17(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f2455]) ).

fof(f3806,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hAPP_nat_real(power_power_real(sK17(X0,X1)),X1) = X0 ),
    inference(cnf_transformation,[],[f2455]) ).

fof(f3807,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK17(X0,X1))) ),
    inference(cnf_transformation,[],[f2455]) ).

fof(f3808,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1))
      | one_one_nat = X0 ),
    inference(cnf_transformation,[],[f2456]) ).

fof(f3810,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X0)),X1))
      | one_one_nat = X0 ),
    inference(cnf_transformation,[],[f2457]) ).

fof(f3812,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    inference(cnf_transformation,[],[f902]) ).

fof(f3815,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f905]) ).

fof(f3816,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
    inference(cnf_transformation,[],[f906]) ).

fof(f3817,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f907]) ).

fof(f3818,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0)) ),
    inference(cnf_transformation,[],[f1878]) ).

fof(f3819,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1880]) ).

fof(f3820,plain,
    ! [X0] : zero_zero_nat = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0),
    inference(cnf_transformation,[],[f910]) ).

fof(f3821,plain,
    ! [X0] : hAPP_nat_nat(minus_minus_nat(X0),zero_zero_nat) = X0,
    inference(cnf_transformation,[],[f911]) ).

fof(f3822,plain,
    ! [X0] : zero_zero_nat = hAPP_nat_nat(minus_minus_nat(X0),X0),
    inference(cnf_transformation,[],[f912]) ).

fof(f3823,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X0),X1)
      | zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1882]) ).

fof(f3836,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2459]) ).

fof(f3840,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f1890]) ).

fof(f3841,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)) ),
    inference(cnf_transformation,[],[f1891]) ).

fof(f3861,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f1921]) ).

fof(f3887,plain,
    ! [X0,X1] :
      ( X0 != X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f2468]) ).

fof(f3889,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2468]) ).

fof(f3891,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1940]) ).

fof(f3892,plain,
    ! [X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(cnf_transformation,[],[f953]) ).

fof(f3893,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2)),
    inference(cnf_transformation,[],[f954]) ).

fof(f3894,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f955]) ).

fof(f3895,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X0),X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f2469]) ).

fof(f3897,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X2),X1)
      | X0 = X2 ),
    inference(cnf_transformation,[],[f2470]) ).

fof(f3899,plain,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X1) = X0,
    inference(cnf_transformation,[],[f958]) ).

fof(f3900,plain,
    ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0) = X1,
    inference(cnf_transformation,[],[f959]) ).

fof(f3901,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f960]) ).

fof(f3902,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
    inference(cnf_transformation,[],[f961]) ).

fof(f3903,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X1)),
    inference(cnf_transformation,[],[f962]) ).

fof(f3905,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f964]) ).

fof(f3907,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f1943]) ).

fof(f3909,plain,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f968]) ).

fof(f3910,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f1946]) ).

fof(f3911,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1947]) ).

fof(f3912,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f1948]) ).

fof(f3913,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),X1)
      | X0 = X2 ),
    inference(cnf_transformation,[],[f2471]) ).

fof(f3915,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) ),
    inference(cnf_transformation,[],[f1952]) ).

fof(f3916,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ),
    inference(cnf_transformation,[],[f2472]) ).

fof(f3918,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f975]) ).

fof(f3919,plain,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    inference(cnf_transformation,[],[f976]) ).

fof(f3920,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f977]) ).

fof(f3921,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(cnf_transformation,[],[f978]) ).

fof(f3925,plain,
    ! [X0] :
      ( zero_zero_nat = X0
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2473]) ).

fof(f3927,plain,
    ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
    inference(cnf_transformation,[],[f983]) ).

fof(f3928,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ),
    inference(cnf_transformation,[],[f1958]) ).

fof(f3929,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f2474]) ).

fof(f3930,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f2474]) ).

fof(f3931,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0
      | zero_zero_nat = X1 ),
    inference(cnf_transformation,[],[f1959]) ).

fof(f3932,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat
      | zero_zero_nat = X1 ),
    inference(cnf_transformation,[],[f2476]) ).

fof(f3933,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2476]) ).

fof(f3935,plain,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0,
    inference(cnf_transformation,[],[f988]) ).

fof(f3936,plain,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0,
    inference(cnf_transformation,[],[f989]) ).

fof(f3937,plain,
    ! [X0,X1] : zero_zero_nat = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(cnf_transformation,[],[f990]) ).

fof(f3938,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2477]) ).

fof(f3940,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    inference(cnf_transformation,[],[f992]) ).

fof(f3942,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(minus_minus_nat(X0),X1)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2478]) ).

fof(f3943,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | zero_zero_nat = hAPP_nat_nat(minus_minus_nat(X0),X1) ),
    inference(cnf_transformation,[],[f2478]) ).

fof(f3946,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != zero_zero_nat
      | zero_zero_nat = X1
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2480]) ).

fof(f3947,plain,
    ! [X0,X1] :
      ( zero_zero_nat != X1
      | hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ),
    inference(cnf_transformation,[],[f2480]) ).

fof(f3948,plain,
    ! [X0,X1] :
      ( zero_zero_nat != X0
      | hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ),
    inference(cnf_transformation,[],[f2480]) ).

fof(f3952,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X2),X1)
      | zero_zero_nat = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f2484]) ).

fof(f3955,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f1000]) ).

fof(f3956,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)),
    inference(cnf_transformation,[],[f1001]) ).

fof(f3957,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2485]) ).

fof(f3958,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f2485]) ).

fof(f3959,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1961]) ).

fof(f3960,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1962]) ).

fof(f3961,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1963]) ).

fof(f3962,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(cnf_transformation,[],[f1965]) ).

fof(f3963,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | hAPP_nat_nat(plus_plus_nat(X2),X1) != hAPP_nat_nat(plus_plus_nat(X0),X3)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1967]) ).

fof(f3964,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f1968]) ).

fof(f3965,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X0 ),
    inference(cnf_transformation,[],[f1969]) ).

fof(f3966,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)) ),
    inference(cnf_transformation,[],[f2486]) ).

fof(f3967,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2486]) ).

fof(f3968,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f2488]) ).

fof(f3975,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | X0 = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1972]) ).

fof(f3976,plain,
    ! [X0,X1] :
      ( X0 != X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1973]) ).

fof(f3977,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1973]) ).

fof(f3978,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ),
    inference(cnf_transformation,[],[f2491]) ).

fof(f3980,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1977]) ).

fof(f3981,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2492]) ).

fof(f3982,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))) ),
    inference(cnf_transformation,[],[f2492]) ).

fof(f3983,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f1979]) ).

fof(f3984,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1981]) ).

fof(f3985,plain,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))),
    inference(cnf_transformation,[],[f1021]) ).

fof(f3987,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f2495]) ).

fof(f3988,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X0),X2) != X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2495]) ).

fof(f3989,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2496]) ).

fof(f3990,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f2496]) ).

fof(f3991,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1982]) ).

fof(f3992,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f1983]) ).

fof(f3993,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X2),X0))) ),
    inference(cnf_transformation,[],[f1984]) ).

fof(f3994,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1))) ),
    inference(cnf_transformation,[],[f1986]) ).

fof(f3997,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f1989]) ).

fof(f3998,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f1989]) ).

fof(f3999,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) ),
    inference(cnf_transformation,[],[f1990]) ).

fof(f4000,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2497]) ).

fof(f4001,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f2497]) ).

fof(f4002,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1))) ),
    inference(cnf_transformation,[],[f1991]) ).

fof(f4003,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ),
    inference(cnf_transformation,[],[f1992]) ).

fof(f4005,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f2498]) ).

fof(f4006,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2498]) ).

fof(f4010,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1) ),
    inference(cnf_transformation,[],[f1997]) ).

fof(f4012,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X0) ),
    inference(cnf_transformation,[],[f1999]) ).

fof(f4013,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f1043]) ).

fof(f4014,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(cnf_transformation,[],[f1044]) ).

fof(f4017,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1))) ),
    inference(cnf_transformation,[],[f2001]) ).

fof(f4020,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)))),
    inference(cnf_transformation,[],[f1049]) ).

fof(f4021,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),X0))),
    inference(cnf_transformation,[],[f1050]) ).

fof(f4025,plain,
    ! [X0] : hAPP_nat_nat(times_times_nat(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f1052]) ).

fof(f4026,plain,
    ! [X0,X1] :
      ( one_one_nat != hAPP_nat_nat(times_times_nat(X0),X1)
      | one_one_nat = X1 ),
    inference(cnf_transformation,[],[f2504]) ).

fof(f4027,plain,
    ! [X0,X1] :
      ( one_one_nat != hAPP_nat_nat(times_times_nat(X0),X1)
      | one_one_nat = X0 ),
    inference(cnf_transformation,[],[f2504]) ).

fof(f4029,plain,
    ! [X0] : hAPP_nat_nat(times_times_nat(one_one_nat),X0) = X0,
    inference(cnf_transformation,[],[f1054]) ).

fof(f4030,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2005]) ).

fof(f4031,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2506]) ).

fof(f4036,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X2),sK19(X0,X1,X2)) = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2510]) ).

fof(f4037,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,sK19(X0,X1,X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2510]) ).

fof(f4038,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X2),sK19(X0,X1,X2)) = X1
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2510]) ).

fof(f4039,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,sK19(X0,X1,X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2510]) ).

fof(f4041,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2514]) ).

fof(f4042,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,sK20(X0,X1,X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2514]) ).

fof(f4043,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X2),sK20(X0,X1,X2)) = X1
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2514]) ).

fof(f4044,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,sK20(X0,X1,X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2514]) ).

fof(f4045,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(X2),sK20(X0,X1,X2)) = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2514]) ).

fof(f4048,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f2516]) ).

fof(f4049,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(cnf_transformation,[],[f2516]) ).

fof(f4050,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2516]) ).

fof(f4051,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2518]) ).

fof(f4052,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2518]) ).

fof(f4054,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(cnf_transformation,[],[f2520]) ).

fof(f4055,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2520]) ).

fof(f4056,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f2520]) ).

fof(f4057,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != X0
      | zero_zero_nat = X0
      | one_one_nat = X1 ),
    inference(cnf_transformation,[],[f2013]) ).

fof(f4058,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2015]) ).

fof(f4061,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f2522]) ).

fof(f4062,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f2522]) ).

fof(f4063,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f2524]) ).

fof(f4064,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2524]) ).

fof(f4065,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2524]) ).

fof(f4066,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(sK21(X0,X1)),one_one_nat))) ),
    inference(cnf_transformation,[],[f2525]) ).

fof(f4067,plain,
    ! [X3,X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK21(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(cnf_transformation,[],[f2525]) ).

fof(f4068,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK21(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f2525]) ).

fof(f4069,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ),
    inference(cnf_transformation,[],[f2526]) ).

fof(f4070,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2))) ),
    inference(cnf_transformation,[],[f2526]) ).

fof(f4071,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X0),X2)
      | X1 = X2
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2528]) ).

fof(f4074,plain,
    ! [X2,X3,X0,X1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f1072]) ).

fof(f4078,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f2530]) ).

fof(f4079,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | zero_zero_nat = X0 ),
    inference(cnf_transformation,[],[f2532]) ).

fof(f4080,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f2532]) ).

fof(f4082,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2533]) ).

fof(f4084,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2534]) ).

fof(f4086,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ),
    inference(cnf_transformation,[],[f2535]) ).

fof(f4087,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2))) ),
    inference(cnf_transformation,[],[f2535]) ).

fof(f4088,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2) ),
    inference(cnf_transformation,[],[f2028]) ).

fof(f4089,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1) = X2 ),
    inference(cnf_transformation,[],[f2536]) ).

fof(f4091,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2))) ),
    inference(cnf_transformation,[],[f2537]) ).

fof(f4092,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2))) ),
    inference(cnf_transformation,[],[f2537]) ).

fof(f4093,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)) ),
    inference(cnf_transformation,[],[f2031]) ).

fof(f4094,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2)
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) = X1 ),
    inference(cnf_transformation,[],[f2538]) ).

fof(f4095,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2) != X1
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2) ),
    inference(cnf_transformation,[],[f2538]) ).

fof(f4096,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2)) ),
    inference(cnf_transformation,[],[f2539]) ).

fof(f4097,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X1)),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),X2))) ),
    inference(cnf_transformation,[],[f2539]) ).

fof(f4098,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X0)))) ),
    inference(cnf_transformation,[],[f2034]) ).

fof(f4099,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X0)))) ),
    inference(cnf_transformation,[],[f2034]) ).

fof(f4100,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | twoSqu1241645765sum2sq(product_Pair_int_int(sK22(X0),sK23(X0))) = X0 ),
    inference(cnf_transformation,[],[f2542]) ).

fof(f4101,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | is_int(sK23(X0)) ),
    inference(cnf_transformation,[],[f2542]) ).

fof(f4102,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | is_int(sK22(X0)) ),
    inference(cnf_transformation,[],[f2542]) ).

fof(f4103,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X0)
      | twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)) != X0
      | ~ is_int(X2)
      | ~ is_int(X1)
      | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(cnf_transformation,[],[f2542]) ).

fof(f4118,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | zero_zero_int = X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f2553]) ).

fof(f4119,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | zero_zero_int = X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2553]) ).

fof(f4121,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | is_int(sK24(X1,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2555]) ).

fof(f4122,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(X1,sK24(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2555]) ).

fof(f4123,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(sK24(X1,X2)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2555]) ).

fof(f4124,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | is_int(sK25(X1,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2557]) ).

fof(f4125,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(X1,sK25(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2557]) ).

fof(f4126,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(sK25(X1,X2)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f2557]) ).

fof(f4127,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(X0)),X0)) ),
    inference(cnf_transformation,[],[f2558]) ).

fof(f4128,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,sK26(X0))) ),
    inference(cnf_transformation,[],[f2558]) ).

fof(f4129,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | is_int(sK26(X0)) ),
    inference(cnf_transformation,[],[f2558]) ).

fof(f4130,plain,
    ! [X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ is_int(X3)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
      | sK27(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f2559]) ).

fof(f4131,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,sK27(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f2559]) ).

fof(f4132,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f2559]) ).

fof(f4133,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK27(X0,X1))) ),
    inference(cnf_transformation,[],[f2559]) ).

fof(f4134,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | is_int(sK27(X0,X1)) ),
    inference(cnf_transformation,[],[f2559]) ).

fof(f4135,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2047]) ).

fof(f4136,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),number_number_of_int(min)),X0)) ),
    inference(cnf_transformation,[],[f2048]) ).

fof(f4137,plain,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | zfact(X0) = hAPP_int_int(times_times_int(X0),zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(cnf_transformation,[],[f2049]) ).

fof(f4138,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
      | one_one_int = zfact(X0) ),
    inference(cnf_transformation,[],[f2049]) ).

fof(f4139,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | inv(X1,inv(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f2051]) ).

fof(f4140,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ),
    inference(cnf_transformation,[],[f2053]) ).

fof(f4141,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X0)),X0)),X1),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3)) ),
    inference(cnf_transformation,[],[f2054]) ).

fof(f4143,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | inv(X1,X0) != X0 ),
    inference(cnf_transformation,[],[f2057]) ).

fof(f4144,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | one_one_int != inv(X1,X0) ),
    inference(cnf_transformation,[],[f2059]) ).

fof(f4145,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hAPP_int_int(minus_minus_int(X1),one_one_int) != inv(X1,X0) ),
    inference(cnf_transformation,[],[f2061]) ).

fof(f4146,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(X1,X0))) ),
    inference(cnf_transformation,[],[f2063]) ).

fof(f4147,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(X1,X0)),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f2065]) ).

fof(f4148,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(multInv(X2,X0),multInv(X2,X1)),X2)) ),
    inference(cnf_transformation,[],[f2067]) ).

fof(f4149,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | zero_zero_int != inv(X1,X0) ),
    inference(cnf_transformation,[],[f2069]) ).

fof(f4150,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X3,X1)),hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3)) ),
    inference(cnf_transformation,[],[f2071]) ).

fof(f4151,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X2,X1),multInv(X2,X0)),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    inference(cnf_transformation,[],[f2073]) ).

fof(f4152,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),X0),X1)) ),
    inference(cnf_transformation,[],[f2075]) ).

fof(f4153,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X1,X0),zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2077]) ).

fof(f4154,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f2079]) ).

fof(f4155,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X2)),X2)),X0),hAPP_int_int(times_times_int(multInv(X3,X2)),X1)),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X3)) ),
    inference(cnf_transformation,[],[f2081]) ).

fof(f4156,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X2)),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),X1),X3)) ),
    inference(cnf_transformation,[],[f2083]) ).

fof(f4157,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X0),multInv(X3,X1))),X3)) ),
    inference(cnf_transformation,[],[f2085]) ).

fof(f4158,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,zero_zero_int),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),multInv(X3,X0)),hAPP_int_int(times_times_int(X2),multInv(X3,X1))),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X3)) ),
    inference(cnf_transformation,[],[f2087]) ).

fof(f4159,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0))),X0),X1)) ),
    inference(cnf_transformation,[],[f2089]) ).

fof(f4160,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0)))),X1)) ),
    inference(cnf_transformation,[],[f2091]) ).

fof(f4162,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X0)),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f2095]) ).

fof(f4163,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(member_int(inv(X2,X0),wset(X1,X2))) ),
    inference(cnf_transformation,[],[f2097]) ).

fof(f4164,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(inv(X2,X0),wset(X1,X2)))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(cnf_transformation,[],[f2099]) ).

fof(f4165,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | hBOOL(member_int(X1,wset(X1,X0))) ),
    inference(cnf_transformation,[],[f2100]) ).

fof(f4166,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | hBOOL(member_int(X0,wset(X2,X1))) ),
    inference(cnf_transformation,[],[f2102]) ).

fof(f4167,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int))) ),
    inference(cnf_transformation,[],[f2104]) ).

fof(f4168,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f2106]) ).

fof(f4169,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X2),one_one_int),X1)))
      | ~ hBOOL(member_int(X0,wset(X2,X1)))
      | inv(X1,X2) = X0
      | X0 = X2 ),
    inference(cnf_transformation,[],[f2108]) ).

fof(f4170,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(cnf_transformation,[],[f2110]) ).

fof(f4171,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | is_int(sK28(X0,X2))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2560]) ).

fof(f4172,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK28(X0,X2)),X2))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2560]) ).

fof(f4173,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(X0,sK28(X0,X2)))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2560]) ).

fof(f4174,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK28(X0,X2)),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2560]) ).

fof(f4175,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | is_int(sK29(X0,X2))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2561]) ).

fof(f4176,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK29(X0,X2)),X2))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2561]) ).

fof(f4177,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,sK29(X0,X2)))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2561]) ).

fof(f4178,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK29(X0,X2)),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2561]) ).

fof(f4179,plain,
    ! [X0,X1] :
      ( is_int(sK30(X1))
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f2562]) ).

fof(f4180,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),sK30(X1)))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(sK30(X1)),one_one_int)))
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f2562]) ).

fof(f4181,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(X1,sK30(X1)))
      | hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f2562]) ).

fof(f4182,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | is_int(sK31(X0,X1))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2563]) ).

fof(f4183,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK31(X0,X1)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2563]) ).

fof(f4184,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(X0,sK31(X0,X1)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2563]) ).

fof(f4185,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK31(X0,X1)),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2563]) ).

fof(f4186,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | is_int(sK32(X0,X1))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2564]) ).

fof(f4187,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sK32(X0,X1)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2564]) ).

fof(f4188,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,sK32(X0,X1)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2564]) ).

fof(f4189,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK32(X0,X1)),one_one_int)))
      | hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(cnf_transformation,[],[f2564]) ).

fof(f4190,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK33(X2)),sK34(X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X2,X0)),X1)),hAPP_nat_nat(X2,hAPP_nat_nat(plus_plus_nat(X0),X1)))) ),
    inference(cnf_transformation,[],[f2565]) ).

fof(f4191,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X2,sK33(X2))),hAPP_nat_nat(X2,sK34(X2))))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X2,X0)),X1)),hAPP_nat_nat(X2,hAPP_nat_nat(plus_plus_nat(X0),X1)))) ),
    inference(cnf_transformation,[],[f2565]) ).

fof(f4192,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(bit0(bit1(pls)))),X0) ),
    inference(cnf_transformation,[],[f2122]) ).

fof(f4193,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,sK35(X0,X1))) ),
    inference(cnf_transformation,[],[f2566]) ).

fof(f4194,plain,
    ! [X3,X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK35(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
    inference(cnf_transformation,[],[f2566]) ).

fof(f4195,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK35(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f2566]) ).

fof(f4197,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(member_int(X1,d22set(X0))) ),
    inference(cnf_transformation,[],[f2126]) ).

fof(f4198,plain,
    ! [X0,X1] :
      ( ~ hBOOL(member_int(X0,d22set(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f2127]) ).

fof(f4199,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(member_int(X1,d22set(X0))) ),
    inference(cnf_transformation,[],[f2129]) ).

fof(f4200,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f2567]) ).

fof(f4201,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK36(X0,X1))) ),
    inference(cnf_transformation,[],[f2567]) ).

fof(f4207,plain,
    ! [X0] :
      ( zero_zero_nat = X0
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2571]) ).

fof(f4210,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)),
    inference(cnf_transformation,[],[f1147]) ).

fof(f4213,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X0)),
    inference(cnf_transformation,[],[f1150]) ).

fof(f4219,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
      | one_one_nat = X0 ),
    inference(cnf_transformation,[],[f2135]) ).

fof(f4220,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2137]) ).

fof(f4221,plain,
    ! [X2,X0,X1] :
      ( zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2575]) ).

fof(f4223,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | zero_zero_nat = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2)) ),
    inference(cnf_transformation,[],[f2140]) ).

fof(f4224,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | zero_zero_nat = X1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2142]) ).

fof(f4225,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | hAPP_nat_nat(times_times_nat(X2),X1) != hAPP_nat_nat(times_times_nat(X2),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f2144]) ).

fof(f4226,plain,
    ! [X0] : sr(X0) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),cOMBC_int_int_bool(ord_less_int,X0))),
    inference(cnf_transformation,[],[f1159]) ).

fof(f4227,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))),one_one_int) ),
    inference(cnf_transformation,[],[f2145]) ).

fof(f4228,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
      | hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) ),
    inference(cnf_transformation,[],[f2146]) ).

fof(f4229,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
      | hAPP_int_int(div_mod_int(number_number_of_int(bit1(X0))),number_number_of_int(bit0(X1))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1)))),one_one_int) ),
    inference(cnf_transformation,[],[f2146]) ).

fof(f4230,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | zero_zero_int = hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)) ),
    inference(cnf_transformation,[],[f2576]) ).

fof(f4231,plain,
    ! [X0,X1] :
      ( zero_zero_int != hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2576]) ).

fof(f4234,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X1),X0))) ),
    inference(cnf_transformation,[],[f2150]) ).

fof(f4235,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),X1)) ),
    inference(cnf_transformation,[],[f2151]) ).

fof(f4236,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | hAPP_int_int(times_times_int(X1),sK37(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f2579]) ).

fof(f4237,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | is_int(sK37(X0,X1)) ),
    inference(cnf_transformation,[],[f2579]) ).

fof(f4238,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(X1),X2) != X0
      | ~ is_int(X2)
      | zero_zero_int = hAPP_int_int(div_mod_int(X0),X1) ),
    inference(cnf_transformation,[],[f2579]) ).

fof(f4239,plain,
    ! [X2,X0,X1] :
      ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2))) ),
    inference(cnf_transformation,[],[f2580]) ).

fof(f4240,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2)))
      | hAPP_int_int(div_mod_int(X0),X1) = hAPP_int_int(div_mod_int(X2),X1) ),
    inference(cnf_transformation,[],[f2580]) ).

fof(f4241,plain,
    ! [X2,X0,X1] :
      ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1)
      | hBOOL(hAPP_int_bool(zcong(X0,X2),X1)) ),
    inference(cnf_transformation,[],[f2153]) ).

fof(f4243,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2)) ),
    inference(cnf_transformation,[],[f2581]) ).

fof(f4244,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f2581]) ).

fof(f4245,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2155]) ).

fof(f4246,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(div_mod_int(X2),X0))) ),
    inference(cnf_transformation,[],[f2157]) ).

fof(f4247,plain,
    ! [X2,X0,X1] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f1174]) ).

fof(f4249,plain,
    ! [X2,X0,X1] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2),
    inference(cnf_transformation,[],[f1176]) ).

fof(f4250,plain,
    ! [X0] : zero_zero_int = hAPP_int_int(div_mod_int(X0),X0),
    inference(cnf_transformation,[],[f1177]) ).

fof(f4251,plain,
    ! [X0] : zero_zero_int = hAPP_int_int(div_mod_int(zero_zero_int),X0),
    inference(cnf_transformation,[],[f1178]) ).

fof(f4252,plain,
    ! [X2,X0,X1] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X1)),X2),
    inference(cnf_transformation,[],[f1179]) ).

fof(f4253,plain,
    ! [X2,X0,X1] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f1180]) ).

fof(f4254,plain,
    ! [X0] : zero_zero_int = hAPP_int_int(div_mod_int(X0),number_number_of_int(min)),
    inference(cnf_transformation,[],[f1181]) ).

fof(f4255,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hAPP_int_int(div_mod_int(X0),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X0),X1)),X2) ),
    inference(cnf_transformation,[],[f2159]) ).

fof(f4261,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(cnf_transformation,[],[f2164]) ).

fof(f4263,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(cnf_transformation,[],[f2166]) ).

fof(f4264,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2166]) ).

fof(f4265,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(cnf_transformation,[],[f2168]) ).

fof(f4266,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X0)),zero_zero_int))
      | hAPP_int_int(plus_plus_int(X1),X0) = hAPP_int_int(div_mod_int(X1),X0) ),
    inference(cnf_transformation,[],[f2170]) ).

fof(f4267,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1))) = hAPP_int_int(div_mod_int(number_number_of_int(bit0(X0))),number_number_of_int(bit0(X1))),
    inference(cnf_transformation,[],[f1191]) ).

fof(f4268,plain,
    ! [X2,X0,X1,X6,X5] :
      ( ~ sP3(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4269,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4270,plain,
    ! [X2,X0,X1] :
      ( is_int(sK39(X0,X1,X2))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4271,plain,
    ! [X2,X0,X1] :
      ( is_int(sK38(X0,X1,X2))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4272,plain,
    ! [X2,X0,X1] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),sK38(X0,X1,X2))),sK39(X0,X1,X2)) = X2
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4273,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK39(X0,X1,X2)),X1))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4274,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK39(X0,X1,X2)))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4275,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(X0,sK39(X0,X1,X2)))
      | sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2586]) ).

fof(f4284,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      | sP2(X0,X2,X1) ),
    inference(cnf_transformation,[],[f2592]) ).

fof(f4285,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      | sP3(X0,X2,X1) ),
    inference(cnf_transformation,[],[f2592]) ).

fof(f4286,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      | zero_zero_int != X2
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2592]) ).

fof(f4287,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ sP2(X0,X2,X1)
      | ~ sP3(X0,X2,X1)
      | zero_zero_int = X2
      | hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(cnf_transformation,[],[f2592]) ).

fof(f4288,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ sP2(X0,X2,X1)
      | ~ sP3(X0,X2,X1)
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(cnf_transformation,[],[f2592]) ).

fof(f4289,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(cnf_transformation,[],[f2174]) ).

fof(f4290,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),hAPP_int_int(times_times_int(X1),X3))) ),
    inference(cnf_transformation,[],[f2176]) ).

fof(f4291,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(cnf_transformation,[],[f2178]) ).

fof(f4292,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f2180]) ).

fof(f4294,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | zero_zero_int = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(cnf_transformation,[],[f2182]) ).

fof(f4295,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
      | zero_zero_int = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(cnf_transformation,[],[f2182]) ).

fof(f4297,plain,
    ! [X0] :
      ( zero_zero_int = hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls))))
      | one_one_int = hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) ),
    inference(cnf_transformation,[],[f2593]) ).

fof(f4298,plain,
    ! [X0] :
      ( one_one_int != hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls))))
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),number_number_of_int(bit0(bit1(pls)))) ),
    inference(cnf_transformation,[],[f2593]) ).

fof(f4299,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) ),
    inference(cnf_transformation,[],[f2183]) ).

fof(f4300,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),X1)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(cnf_transformation,[],[f2184]) ).

fof(f4301,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | hAPP_int_int(times_times_int(X1),sK42(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f2594]) ).

fof(f4302,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | zero_zero_int != hAPP_int_int(div_mod_int(X0),X1)
      | is_int(sK42(X0,X1)) ),
    inference(cnf_transformation,[],[f2594]) ).

fof(f4303,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(X2,X0)),standardRes(X2,X1)),hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f2187]) ).

fof(f4304,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    inference(cnf_transformation,[],[f2188]) ).

fof(f4305,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1)) ),
    inference(cnf_transformation,[],[f2189]) ).

fof(f4306,plain,
    ! [X0,X1] :
      ( zero_zero_nat != hAPP_nat_nat(div_mod_nat(X0),X1)
      | hAPP_nat_nat(times_times_nat(X1),sK43(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f2597]) ).

fof(f4307,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(times_times_nat(X1),X2) != X0
      | zero_zero_nat = hAPP_nat_nat(div_mod_nat(X0),X1) ),
    inference(cnf_transformation,[],[f2597]) ).

fof(f4309,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(div_mod_nat(X0),X1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X1) ),
    inference(cnf_transformation,[],[f2191]) ).

fof(f4311,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),X1) = hAPP_nat_nat(div_mod_nat(X2),X1),
    inference(cnf_transformation,[],[f1208]) ).

fof(f4312,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | hAPP_nat_nat(div_mod_nat(X1),X0) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X0) ),
    inference(cnf_transformation,[],[f2192]) ).

fof(f4313,plain,
    ! [X0,X1] : standardRes(X0,X1) = hAPP_int_int(div_mod_int(X1),X0),
    inference(cnf_transformation,[],[f1210]) ).

fof(f4314,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X2) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f1211]) ).

fof(f4315,plain,
    ! [X2,X0,X1] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(div_mod_nat(X1),X2)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(cnf_transformation,[],[f1212]) ).

fof(f4316,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f2193]) ).

fof(f4317,plain,
    ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f1214]) ).

fof(f4320,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
      | zero_zero_int != standardRes(X1,X0) ),
    inference(cnf_transformation,[],[f2599]) ).

fof(f4321,plain,
    ! [X0,X1] :
      ( zero_zero_int = standardRes(X1,X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2599]) ).

fof(f4322,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,standardRes(X1,X0)),X1)),
    inference(cnf_transformation,[],[f1217]) ).

fof(f4323,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(X1,X0)),X1)) ),
    inference(cnf_transformation,[],[f2194]) ).

fof(f4324,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(member_int(X0,sr(X1)))
      | standardRes(X1,X0) = X0 ),
    inference(cnf_transformation,[],[f2196]) ).

fof(f4335,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
      | sP4(X1,X0,X2) ),
    inference(cnf_transformation,[],[f2604]) ).

fof(f4336,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X1,X0,X2)
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f2604]) ).

fof(f4337,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X3))),X1)),hAPP_nat_nat(times_times_nat(X2),X3))) ),
    inference(cnf_transformation,[],[f2200]) ).

fof(f4338,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(X1,X0))) ),
    inference(cnf_transformation,[],[f2201]) ).

fof(f4340,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | standardRes(X2,X0) = standardRes(X2,X1) ),
    inference(cnf_transformation,[],[f2605]) ).

fof(f4341,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f1224]) ).

fof(f4342,plain,
    ! [X0,X1] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f1225]) ).

fof(f4343,plain,
    ! [X0,X1] :
      ( hBOOL(X1)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f1226]) ).

fof(f4344,plain,
    ! [X2,X0,X1] : hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1),
    inference(cnf_transformation,[],[f1227]) ).

fof(f4345,plain,
    ! [X2,X0,X1] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)),
    inference(cnf_transformation,[],[f1228]) ).

fof(f4346,plain,
    ! [X2,X0,X1] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)),
    inference(cnf_transformation,[],[f1229]) ).

fof(f4347,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
    inference(cnf_transformation,[],[f2203]) ).

fof(f4348,plain,
    ! [X0] : sr(X0) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),cOMBC_int_int_bool(ord_less_int,X0))),
    inference(definition_unfolding,[],[f4226,f3091]) ).

fof(f4353,plain,
    ( one_one_int != t
    | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
    inference(definition_unfolding,[],[f2632,f2913,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4354,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
    inference(definition_unfolding,[],[f2635,f2913,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4355,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f2638,f2913,f2913,f2960]) ).

fof(f4356,plain,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f2639,f2913,f2913,f2960]) ).

fof(f4357,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
    inference(definition_unfolding,[],[f2640,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4358,plain,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t))),
    inference(definition_unfolding,[],[f2641,f2913,f2913,f2960]) ).

fof(f4360,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f2643,f2960,f2960,f2960,f2960,f2960,f2960,f2913,f2960,f2960,f2960,f2913,f2960,f2960,f2960]) ).

fof(f4361,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)),
    inference(definition_unfolding,[],[f2644,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4362,plain,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)),
    inference(definition_unfolding,[],[f2645,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4363,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)),
    inference(definition_unfolding,[],[f2646,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4367,plain,
    ! [X0] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f2650,f2960,f2960,f2913,f2960]) ).

fof(f4371,plain,
    ! [X0] : hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2654,f2913,f2960]) ).

fof(f4372,plain,
    ! [X0] : hAPP_real_real(times_times_real(X0),X0) = hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2655,f2913,f2960]) ).

fof(f4373,plain,
    ! [X0] : hAPP_nat_nat(times_times_nat(X0),X0) = hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2656,f2913,f2960]) ).

fof(f4377,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X1)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(definition_unfolding,[],[f2660,f2913,f2960]) ).

fof(f4378,plain,
    ! [X0,X1] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X1)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(definition_unfolding,[],[f2661,f2913,f2960]) ).

fof(f4379,plain,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(definition_unfolding,[],[f2662,f2913,f2960]) ).

fof(f4380,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)),
    inference(definition_unfolding,[],[f2663,f2960]) ).

fof(f4381,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)),
    inference(definition_unfolding,[],[f2664,f2960]) ).

fof(f4382,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
    inference(definition_unfolding,[],[f2665,f2960]) ).

fof(f4383,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
    inference(definition_unfolding,[],[f2666,f2960]) ).

fof(f4386,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),sK9),
    inference(definition_unfolding,[],[f2670,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4388,plain,
    ! [X0] : hAPP_nat_nat(plus_plus_nat(X0),X0) = hAPP_nat_nat(times_times_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2706,f2913,f2960]) ).

fof(f4389,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
    inference(definition_unfolding,[],[f2707,f2913,f2960]) ).

fof(f4392,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(definition_unfolding,[],[f2711,f2960,f2960]) ).

fof(f4393,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2710,f2960,f2960]) ).

fof(f4396,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(definition_unfolding,[],[f2715,f2960,f2960]) ).

fof(f4397,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2714,f2960,f2960]) ).

fof(f4400,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(definition_unfolding,[],[f2720,f2913,f2913]) ).

fof(f4401,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2719,f2913,f2913]) ).

fof(f4404,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(definition_unfolding,[],[f2725,f2913,f2913]) ).

fof(f4405,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2724,f2913,f2913]) ).

fof(f4406,plain,
    one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),
    inference(definition_unfolding,[],[f2735,f2960]) ).

fof(f4408,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(definition_unfolding,[],[f2738,f2960]) ).

fof(f4409,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f2737,f2960]) ).

fof(f4410,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f2740,f2960]) ).

fof(f4411,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f2739,f2960]) ).

fof(f4414,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(definition_unfolding,[],[f2744,f2960,f2913]) ).

fof(f4415,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2743,f2960,f2913]) ).

fof(f4418,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(definition_unfolding,[],[f2748,f2913,f2960]) ).

fof(f4419,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2747,f2913,f2960]) ).

fof(f4420,plain,
    hBOOL(hAPP_int_bool(zprime,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f2754,f2913,f2960]) ).

fof(f4422,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)
      | X0 = X1 ),
    inference(definition_unfolding,[],[f2811,f2960,f2960]) ).

fof(f4424,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(X1),X1)
      | X0 = X1 ),
    inference(definition_unfolding,[],[f2813,f2913,f2913]) ).

fof(f4429,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(definition_unfolding,[],[f2826,f2960,f2913]) ).

fof(f4430,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2825,f2960,f2913]) ).

fof(f4433,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(definition_unfolding,[],[f2830,f2913]) ).

fof(f4434,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f2829,f2913]) ).

fof(f4435,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f2832,f2960]) ).

fof(f4436,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f2831,f2960]) ).

fof(f4439,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(definition_unfolding,[],[f2836,f2913,f2960]) ).

fof(f4440,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f2835,f2913,f2960]) ).

fof(f4441,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(definition_unfolding,[],[f2838,f2913]) ).

fof(f4442,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(definition_unfolding,[],[f2837,f2913]) ).

fof(f4443,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(definition_unfolding,[],[f2840,f2913]) ).

fof(f4444,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f2839,f2913]) ).

fof(f4445,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2844,f2913,f2960,f2913,f2960]) ).

fof(f4446,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2845,f2913,f2960,f2913,f2960]) ).

fof(f4447,plain,
    ! [X0,X1] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2846,f2913,f2960,f2913,f2960]) ).

fof(f4448,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ),
    inference(definition_unfolding,[],[f2848,f2960]) ).

fof(f4449,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(definition_unfolding,[],[f2847,f2960]) ).

fof(f4450,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(definition_unfolding,[],[f2850,f2960]) ).

fof(f4451,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(definition_unfolding,[],[f2849,f2960]) ).

fof(f4452,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f2852,f2960]) ).

fof(f4453,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(definition_unfolding,[],[f2851,f2960]) ).

fof(f4454,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(definition_unfolding,[],[f2854,f2960]) ).

fof(f4455,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(definition_unfolding,[],[f2853,f2960]) ).

fof(f4456,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int)) ),
    inference(definition_unfolding,[],[f2856,f2960]) ).

fof(f4457,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(definition_unfolding,[],[f2855,f2960]) ).

fof(f4458,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(definition_unfolding,[],[f2858,f2960]) ).

fof(f4459,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(definition_unfolding,[],[f2857,f2960]) ).

fof(f4460,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f2860,f2960]) ).

fof(f4461,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(definition_unfolding,[],[f2859,f2960]) ).

fof(f4462,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(definition_unfolding,[],[f2862,f2960]) ).

fof(f4463,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(definition_unfolding,[],[f2861,f2960]) ).

fof(f4464,plain,
    ! [X0] : pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
    inference(definition_unfolding,[],[f2899,f2960]) ).

fof(f4466,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(definition_unfolding,[],[f2901,f2960,f2913]) ).

fof(f4472,plain,
    pls = hAPP_int_int(plus_plus_int(pls),pls),
    inference(definition_unfolding,[],[f2907,f2913]) ).

fof(f4475,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(definition_unfolding,[],[f2926,f2913,f2960]) ).

fof(f4477,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X1))),hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),
    inference(definition_unfolding,[],[f2959,f2960,f2913,f2960]) ).

fof(f4478,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(definition_unfolding,[],[f2961,f2960]) ).

fof(f4479,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0))),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(definition_unfolding,[],[f2962,f2960]) ).

fof(f4484,plain,
    one_one_int = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),
    inference(definition_unfolding,[],[f2967,f2960]) ).

fof(f4486,plain,
    one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),
    inference(definition_unfolding,[],[f2969,f2960]) ).

fof(f4492,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),X1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X1))),X1),
    inference(definition_unfolding,[],[f2975,f2960,f2913]) ).

fof(f4493,plain,
    ! [X0] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(definition_unfolding,[],[f2976,f2913]) ).

fof(f4494,plain,
    ! [X0] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(definition_unfolding,[],[f2977,f2913]) ).

fof(f4495,plain,
    ! [X0] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2978,f2960,f2960]) ).

fof(f4496,plain,
    ! [X0] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),X0) = hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2979,f2960,f2960]) ).

fof(f4497,plain,
    ! [X0] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X0)),X0) = hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2980,f2960,f2960]) ).

fof(f4498,plain,
    ! [X0] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f2981,f2913,f2960,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4504,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2987,f2913,f2960]) ).

fof(f4506,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(X0),X0) = hAPP_real_real(times_times_real(X0),number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f2989,f2913,f2960]) ).

fof(f4512,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f2995,f3091,f2913,f2913,f2960]) ).

fof(f4513,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int))),
    inference(definition_unfolding,[],[f2996,f2913,f2913,f2960,f2913,f2960]) ).

fof(f4514,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = X0
      | number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)) ),
    inference(definition_unfolding,[],[f2997,f2960,f2913,f2960,f2960,f2960,f2913,f2960]) ).

fof(f4515,plain,
    twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
    inference(definition_unfolding,[],[f2998,f2913,f2913,f2960]) ).

fof(f4517,plain,
    ! [X0] : hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(definition_unfolding,[],[f3000,f2913,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4518,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(s1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3016,f2913,f2960,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4519,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)),
    inference(definition_unfolding,[],[f3019,f3091]) ).

fof(f4520,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3018,f2913,f2913,f2960]) ).

fof(f4521,plain,
    hBOOL(hAPP_int_bool(zcong(s1,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3017,f2913,f2913,f2960]) ).

fof(f4522,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK10)),
    inference(definition_unfolding,[],[f3023,f3091]) ).

fof(f4523,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3022,f2913,f2913,f2960]) ).

fof(f4524,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3021,f2913,f2913,f2960]) ).

fof(f4525,plain,
    ! [X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(s1,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | sK10 = X1 ),
    inference(definition_unfolding,[],[f3020,f3091,f2913,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4526,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK11)),
    inference(definition_unfolding,[],[f3028,f3091]) ).

fof(f4527,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3027,f2913,f2913,f2960]) ).

fof(f4528,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3026,f2913,f2913,f2960]) ).

fof(f4529,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3029,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4533,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X2),X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | X0 = X2 ),
    inference(definition_unfolding,[],[f3048,f3091,f3091]) ).

fof(f4534,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(definition_unfolding,[],[f3051,f3091]) ).

fof(f4535,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f3052,f3091,f3091]) ).

fof(f4537,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | pls = X1
      | pls != hAPP_nat_int(power_power_int(X1),X0) ),
    inference(definition_unfolding,[],[f3057,f3091,f3091]) ).

fof(f4539,plain,
    ! [X0] :
      ( zero_zero_nat = X0
      | pls = hAPP_nat_int(power_power_int(pls),X0) ),
    inference(definition_unfolding,[],[f3059,f3091,f3091]) ).

fof(f4541,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(definition_unfolding,[],[f3066,f3091]) ).

fof(f4547,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),X1) != X0
      | pls = X1 ),
    inference(definition_unfolding,[],[f3081,f3091]) ).

fof(f4549,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | pls != hAPP_int_int(plus_plus_int(X0),X0)
      | pls = X0 ),
    inference(definition_unfolding,[],[f3087,f3091,f3091]) ).

fof(f4551,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(pls),X0) = X0 ),
    inference(definition_unfolding,[],[f3093,f3091]) ).

fof(f4552,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(X0),pls) = X0 ),
    inference(definition_unfolding,[],[f3094,f3091]) ).

fof(f4554,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X0)),hAPP_nat_int(power_power_int(X2),X0))) ),
    inference(definition_unfolding,[],[f3098,f3091]) ).

fof(f4555,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3101,f3091,f3091]) ).

fof(f4556,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(definition_unfolding,[],[f3109,f3091]) ).

fof(f4557,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(definition_unfolding,[],[f3112,f3091]) ).

fof(f4558,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(definition_unfolding,[],[f3115,f3091]) ).

fof(f4562,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3123,f3091,f3091]) ).

fof(f4563,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))
      | pls = X1 ),
    inference(definition_unfolding,[],[f3122,f3091,f3091]) ).

fof(f4564,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ is_int(X4)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X4
      | X0 = X1
      | X2 != X3
      | hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(X4),X0)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) ),
    inference(definition_unfolding,[],[f3128,f3091]) ).

fof(f4565,plain,
    pls = number_number_of_int(pls),
    inference(definition_unfolding,[],[f3132,f3091]) ).

fof(f4570,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(definition_unfolding,[],[f3141,f3091]) ).

fof(f4571,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(definition_unfolding,[],[f3143,f2913,f3091,f3091]) ).

fof(f4572,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f3142,f3091,f2913,f3091]) ).

fof(f4573,plain,
    pls = number_number_of_int(pls),
    inference(definition_unfolding,[],[f3144,f3091]) ).

fof(f4574,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
    inference(definition_unfolding,[],[f3145,f3091]) ).

fof(f4575,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3146,f3091,f3091,f3091]) ).

fof(f4579,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(definition_unfolding,[],[f3154,f3091]) ).

fof(f4581,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3157,f3091,f3091]) ).

fof(f4582,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls))
      | pls = X1 ),
    inference(definition_unfolding,[],[f3156,f3091,f3091]) ).

fof(f4583,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls)),
    inference(definition_unfolding,[],[f3166,f3091]) ).

fof(f4584,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(definition_unfolding,[],[f3170,f3091,f3091]) ).

fof(f4585,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(definition_unfolding,[],[f3169,f3091,f3091]) ).

fof(f4587,plain,
    ! [X0] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),number_number_of_int(X0))),number_number_of_int(X0)),
    inference(definition_unfolding,[],[f3177,f2913,f3091]) ).

fof(f4589,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(definition_unfolding,[],[f3183,f3091]) ).

fof(f4590,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3182,f3091]) ).

fof(f4592,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | one_one_int != hAPP_int_int(times_times_int(X1),X0)
      | one_one_int = X1 ),
    inference(definition_unfolding,[],[f3185,f3091]) ).

fof(f4593,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | one_one_int != hAPP_int_int(times_times_int(X1),X0)
      | one_one_int = X0 ),
    inference(definition_unfolding,[],[f3184,f3091]) ).

fof(f4594,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(definition_unfolding,[],[f3188,f3091,f3091]) ).

fof(f4595,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f3187,f3091,f3091]) ).

fof(f4596,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f3190,f3091]) ).

fof(f4597,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3189,f3091]) ).

fof(f4598,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(definition_unfolding,[],[f3194,f3091]) ).

fof(f4599,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f3193,f3091]) ).

fof(f4600,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f3200,f3091]) ).

fof(f4601,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3199,f3091]) ).

fof(f4602,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
    inference(definition_unfolding,[],[f3204,f3091]) ).

fof(f4603,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(definition_unfolding,[],[f3203,f3091]) ).

fof(f4604,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),X0))) ),
    inference(definition_unfolding,[],[f3205,f3091,f3091]) ).

fof(f4612,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(definition_unfolding,[],[f3213,f2913,f2960]) ).

fof(f4613,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(definition_unfolding,[],[f3214,f3091,f2913,f2960]) ).

fof(f4614,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(definition_unfolding,[],[f3215,f2913,f2960,f2913,f2960]) ).

fof(f4615,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(definition_unfolding,[],[f3216,f2913,f2960,f2913,f2960]) ).

fof(f4616,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f3217,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4617,plain,
    ! [X0,X1] :
      ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f3218,f2913,f2960,f2913,f2960]) ).

fof(f4618,plain,
    ! [X0,X1] :
      ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f3219,f2913,f2960,f2913,f2960]) ).

fof(f4619,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f3220,f3091,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4620,plain,
    ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),zero_zero_real)),
    inference(definition_unfolding,[],[f3221,f2913,f2960]) ).

fof(f4621,plain,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),pls)),
    inference(definition_unfolding,[],[f3222,f2913,f2960,f3091]) ).

fof(f4622,plain,
    ! [X0] :
      ( zero_zero_real = X0
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(definition_unfolding,[],[f3224,f2913,f2960]) ).

fof(f4624,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | pls = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(definition_unfolding,[],[f3226,f3091,f2913,f2960,f3091]) ).

fof(f4630,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3231,f3091,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4631,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))
      | pls = X1 ),
    inference(definition_unfolding,[],[f3230,f3091,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4635,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
    inference(definition_unfolding,[],[f3251,f2913,f2960,f2913,f2960]) ).

fof(f4636,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
    inference(definition_unfolding,[],[f3252,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4638,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real))
      | zero_zero_real = X0 ),
    inference(definition_unfolding,[],[f3254,f2913,f2960,f2913,f2960]) ).

fof(f4639,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real))
      | zero_zero_real = X1 ),
    inference(definition_unfolding,[],[f3253,f2913,f2960,f2913,f2960]) ).

fof(f4641,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3257,f3091,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4642,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls))
      | pls = X1 ),
    inference(definition_unfolding,[],[f3256,f3091,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4643,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)),
    inference(definition_unfolding,[],[f3259,f2913,f2960,f2913,f2960]) ).

fof(f4644,plain,
    ! [X0,X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls)),
    inference(definition_unfolding,[],[f3260,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4645,plain,
    ! [X0,X1] :
      ( zero_zero_real = X0
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) ),
    inference(definition_unfolding,[],[f3263,f2913,f2960,f2913,f2960]) ).

fof(f4646,plain,
    ! [X0,X1] :
      ( zero_zero_real = X1
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) ),
    inference(definition_unfolding,[],[f3262,f2913,f2960,f2913,f2960]) ).

fof(f4648,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X0
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) ),
    inference(definition_unfolding,[],[f3266,f3091,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4649,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) ),
    inference(definition_unfolding,[],[f3265,f3091,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4651,plain,
    ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)))),
    inference(definition_unfolding,[],[f3267,f2913,f2960]) ).

fof(f4652,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)))),
    inference(definition_unfolding,[],[f3268,f3091,f2913,f2960]) ).

fof(f4653,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3293,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4654,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0)) ),
    inference(definition_unfolding,[],[f3294,f2913,f2960,f3091]) ).

fof(f4655,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))
      | one_one_int = X0
      | pls = X0 ),
    inference(definition_unfolding,[],[f3295,f3091,f2913,f2960,f3091]) ).

fof(f4656,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),zero_zero_real))
      | zero_zero_real = X0 ),
    inference(definition_unfolding,[],[f3296,f2913,f2960]) ).

fof(f4657,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),pls))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3297,f3091,f2913,f2960,f3091]) ).

fof(f4658,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK12(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(definition_unfolding,[],[f3302,f3091]) ).

fof(f4659,plain,
    ! [X2,X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | X0 = X2
      | one_one_int = X2 ),
    inference(definition_unfolding,[],[f3298,f3091]) ).

fof(f4660,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int)) ),
    inference(definition_unfolding,[],[f3305,f3091,f3091]) ).

fof(f4661,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X1)) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
    inference(definition_unfolding,[],[f3306,f3091]) ).

fof(f4662,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3307,f3091,f2913,f2960]) ).

fof(f4663,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK13),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(definition_unfolding,[],[f3309,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4664,plain,
    one_one_int = legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),
    inference(definition_unfolding,[],[f3310,f2913,f2913,f2960]) ).

fof(f4665,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | min != X0
      | min = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
    inference(definition_unfolding,[],[f3322,f2960]) ).

fof(f4666,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | min != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)
      | min = X0 ),
    inference(definition_unfolding,[],[f3321,f2960]) ).

fof(f4669,plain,
    min = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),min)),min),
    inference(definition_unfolding,[],[f3325,f2960]) ).

fof(f4671,plain,
    ! [X0] : min != hAPP_int_int(plus_plus_int(X0),X0),
    inference(definition_unfolding,[],[f3329,f2913]) ).

fof(f4672,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(definition_unfolding,[],[f3335,f2960]) ).

fof(f4673,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(definition_unfolding,[],[f3334,f2960]) ).

fof(f4674,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f3337,f2960]) ).

fof(f4675,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(definition_unfolding,[],[f3336,f2960]) ).

fof(f4676,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(definition_unfolding,[],[f3341,f2913]) ).

fof(f4677,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(definition_unfolding,[],[f3340,f2913]) ).

fof(f4678,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
    inference(definition_unfolding,[],[f3342,f3091]) ).

fof(f4679,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(definition_unfolding,[],[f3344,f2960]) ).

fof(f4680,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(definition_unfolding,[],[f3343,f2960]) ).

fof(f4681,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f3346,f2960]) ).

fof(f4682,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(definition_unfolding,[],[f3345,f2960]) ).

fof(f4683,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(definition_unfolding,[],[f3350,f2913]) ).

fof(f4684,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(definition_unfolding,[],[f3349,f2913]) ).

fof(f4685,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(definition_unfolding,[],[f3362,f2913]) ).

fof(f4686,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(definition_unfolding,[],[f3361,f2913]) ).

fof(f4687,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(definition_unfolding,[],[f3364,f2913]) ).

fof(f4688,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(definition_unfolding,[],[f3363,f2913]) ).

fof(f4689,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3391,f2913,f2960]) ).

fof(f4692,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),pls))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f3401,f3091]) ).

fof(f4693,plain,
    ! [X0] : one_one_real = hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),
    inference(definition_unfolding,[],[f3409,f2913,f2960]) ).

fof(f4694,plain,
    ! [X0] : one_one_int = hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),
    inference(definition_unfolding,[],[f3410,f2913,f2960]) ).

fof(f4697,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | pls != hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1))
      | number_number_of_nat(X1) != zero_zero_nat ),
    inference(definition_unfolding,[],[f3417,f3091]) ).

fof(f4698,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
    inference(definition_unfolding,[],[f3420,f3091]) ).

fof(f4700,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3422,f3091,f3091,f3091]) ).

fof(f4701,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1)) ),
    inference(definition_unfolding,[],[f3423,f3091,f3091]) ).

fof(f4702,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3424,f3091,f3091]) ).

fof(f4703,plain,
    ! [X0] :
      ( number_number_of_nat(X0) != zero_zero_nat
      | one_one_int = hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) ),
    inference(definition_unfolding,[],[f3433,f3091]) ).

fof(f4704,plain,
    ! [X0] :
      ( number_number_of_nat(X0) = zero_zero_nat
      | pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) ),
    inference(definition_unfolding,[],[f3432,f3091,f3091]) ).

fof(f4705,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X0),X1))
      | X0 = X2 ),
    inference(definition_unfolding,[],[f3434,f3091,f3091]) ).

fof(f4707,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3436,f3091,f2960,f2960]) ).

fof(f4708,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
    inference(definition_unfolding,[],[f3437,f3091,f3091,f3091]) ).

fof(f4709,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ),
    inference(definition_unfolding,[],[f3438,f3091]) ).

fof(f4710,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4)) ),
    inference(definition_unfolding,[],[f3439,f3091,f3091,f3091]) ).

fof(f4711,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
    inference(definition_unfolding,[],[f3440,f3091]) ).

fof(f4712,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
    inference(definition_unfolding,[],[f3441,f3091,f3091,f3091,f3091]) ).

fof(f4713,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
    inference(definition_unfolding,[],[f3442,f3091,f3091,f3091]) ).

fof(f4715,plain,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),number_number_of_int(min))),
    inference(definition_unfolding,[],[f3444,f2913,f2913,f2960]) ).

fof(f4717,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2))
      | hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) ),
    inference(definition_unfolding,[],[f3446,f2913,f2960]) ).

fof(f4718,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,number_number_of_int(min)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(definition_unfolding,[],[f3447,f2913,f2960]) ).

fof(f4719,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0)) ),
    inference(definition_unfolding,[],[f3448,f2913,f2960]) ).

fof(f4720,plain,
    hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),number_number_of_int(min)),
    inference(definition_unfolding,[],[f3449,f2913,f2960,f2913,f2960]) ).

fof(f4721,plain,
    ( hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),number_number_of_int(min)))
    | one_one_int != legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)) ),
    inference(definition_unfolding,[],[f3450,f2913,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4723,plain,
    ! [X0,X1] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(X0),X1))),hAPP_int_int(minus_minus_int(X0),X1)),
    inference(definition_unfolding,[],[f3464,f2960,f2913,f2960]) ).

fof(f4724,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),
    inference(definition_unfolding,[],[f3465,f2913,f2960,f2960]) ).

fof(f4725,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(pls),X0)),hAPP_int_int(minus_minus_int(pls),X0)),
    inference(definition_unfolding,[],[f3466,f2913,f2913]) ).

fof(f4726,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f3468,f3091]) ).

fof(f4727,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls)) ),
    inference(definition_unfolding,[],[f3467,f3091]) ).

fof(f4728,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = X1
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(definition_unfolding,[],[f3474,f3091]) ).

fof(f4729,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(min),X0))),hAPP_int_int(minus_minus_int(min),X0)),
    inference(definition_unfolding,[],[f3477,f2960,f2960]) ).

fof(f4730,plain,
    ! [X0] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(min),X0))),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(definition_unfolding,[],[f3478,f2960,f2913]) ).

fof(f4731,plain,
    ! [X0] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),X0)),hAPP_int_int(minus_minus_int(min),X0)),
    inference(definition_unfolding,[],[f3479,f2960,f2913]) ).

fof(f4732,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1)) ),
    inference(definition_unfolding,[],[f3484,f3091]) ).

fof(f4733,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1))
      | hAPP_int_int(minus_minus_int(X1),one_one_int) = X0
      | one_one_int = X0 ),
    inference(definition_unfolding,[],[f3485,f3091]) ).

fof(f4734,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3486,f2913,f2960,f2913,f2960]) ).

fof(f4735,plain,
    ! [X0] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)),
    inference(definition_unfolding,[],[f3487,f3091]) ).

fof(f4736,plain,
    ! [X0,X1] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)),
    inference(definition_unfolding,[],[f3494,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4737,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)),
    inference(definition_unfolding,[],[f3495,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4738,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3496,f2913,f2960,f2913,f2960,f2913,f2960,f2913,f2960]) ).

fof(f4739,plain,
    ! [X0,X1] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3497,f2960,f2960,f2960,f2960,f2960,f2960,f2913,f2960,f2960,f2960,f2913,f2960,f2960,f2960]) ).

fof(f4740,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | X1 = X2 ),
    inference(definition_unfolding,[],[f3498,f3091,f3091,f3091]) ).

fof(f4741,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,pls),X0)) ),
    inference(definition_unfolding,[],[f3499,f3091,f3091]) ).

fof(f4742,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
    inference(definition_unfolding,[],[f3500,f3091]) ).

fof(f4745,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(definition_unfolding,[],[f3504,f3091]) ).

fof(f4746,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
    inference(definition_unfolding,[],[f3503,f3091]) ).

fof(f4747,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | pls = X1 ),
    inference(definition_unfolding,[],[f3506,f3091,f3091,f3091]) ).

fof(f4748,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X0),pls),X2)) ),
    inference(definition_unfolding,[],[f3509,f3091,f3091,f3091]) ).

fof(f4751,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int)))
      | one_one_int = legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int)) ),
    inference(definition_unfolding,[],[f3513,f2913,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4752,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | pls = legendre(X0,X1) ),
    inference(definition_unfolding,[],[f3516,f3091,f3091]) ).

fof(f4753,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(quadRes(X1),X0))
      | one_one_int = legendre(X0,X1) ),
    inference(definition_unfolding,[],[f3515,f3091]) ).

fof(f4754,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(quadRes(X1),X0))
      | legendre(X0,X1) = number_number_of_int(min) ),
    inference(definition_unfolding,[],[f3514,f3091]) ).

fof(f4755,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1))
      | X0 = X1
      | zero_zero_nat = X1 ),
    inference(definition_unfolding,[],[f3517,f2913,f2960]) ).

fof(f4756,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X0))
      | ~ is_int(X2)
      | hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(definition_unfolding,[],[f3520,f2913,f2960]) ).

fof(f4757,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(quadRes(X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X0)) ),
    inference(definition_unfolding,[],[f3518,f2913,f2960]) ).

fof(f4759,plain,
    ! [X0,X1] :
      ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))
      | zero_zero_real = X0 ),
    inference(definition_unfolding,[],[f3522,f2913,f2960,f2913,f2960]) ).

fof(f4760,plain,
    ! [X0,X1] :
      ( zero_zero_real != hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))
      | zero_zero_real = X1 ),
    inference(definition_unfolding,[],[f3521,f2913,f2960,f2913,f2960]) ).

fof(f4761,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | one_one_int != hAPP_int_int(plus_plus_int(X1),X0)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(times_times_int(X0),X2))),X4)) ),
    inference(definition_unfolding,[],[f3525,f3091,f3091]) ).

fof(f4762,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),pls)),
    inference(definition_unfolding,[],[f3528,f3091]) ).

fof(f4763,plain,
    ! [X0,X1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f3560,f2913,f2960,f2913,f2960]) ).

fof(f4768,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ is_int(X0)
      | pls != hAPP_int_int(times_times_int(X0),X1)
      | pls = X1
      | pls = X0 ),
    inference(definition_unfolding,[],[f3570,f3091,f3091,f3091]) ).

fof(f4769,plain,
    ! [X0] : pls = hAPP_int_int(times_times_int(X0),pls),
    inference(definition_unfolding,[],[f3575,f3091,f3091]) ).

fof(f4770,plain,
    ! [X0] : pls = hAPP_int_int(times_times_int(pls),X0),
    inference(definition_unfolding,[],[f3578,f3091,f3091]) ).

fof(f4772,plain,
    one_one_int != pls,
    inference(definition_unfolding,[],[f3584,f3091]) ).

fof(f4773,plain,
    ! [X0] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),X0))
      | pls = X0 ),
    inference(definition_unfolding,[],[f3593,f3091,f3091]) ).

fof(f4774,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),pls)) ),
    inference(definition_unfolding,[],[f3648,f3091,f3091,f3091]) ).

fof(f4775,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),pls)) ),
    inference(definition_unfolding,[],[f3647,f3091,f3091,f3091]) ).

fof(f4778,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(definition_unfolding,[],[f3655,f3091,f3091]) ).

fof(f4779,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1))) ),
    inference(definition_unfolding,[],[f3658,f3091,f3091]) ).

fof(f4780,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(definition_unfolding,[],[f3660,f3091]) ).

fof(f4781,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3662,f3091]) ).

fof(f4782,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(definition_unfolding,[],[f3665,f3091]) ).

fof(f4784,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0))) ),
    inference(definition_unfolding,[],[f3671,f3091]) ).

fof(f4793,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3694,f3091,f3091,f3091]) ).

fof(f4794,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
    inference(definition_unfolding,[],[f3693,f3091,f3091,f3091]) ).

fof(f4796,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(definition_unfolding,[],[f3709,f3091,f3091,f3091]) ).

fof(f4797,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(definition_unfolding,[],[f3708,f3091,f3091,f3091]) ).

fof(f4799,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3706,f3091,f3091,f3091]) ).

fof(f4800,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
    inference(definition_unfolding,[],[f3705,f3091,f3091,f3091]) ).

fof(f4802,plain,
    ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X0))),
    inference(definition_unfolding,[],[f3711,f3091]) ).

fof(f4808,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3726,f3091,f3091,f3091]) ).

fof(f4809,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),pls)) ),
    inference(definition_unfolding,[],[f3729,f3091,f3091,f3091]) ).

fof(f4811,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(definition_unfolding,[],[f3732,f3091]) ).

fof(f4812,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3736,f3091,f3091,f3091]) ).

fof(f4815,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),pls)) ),
    inference(definition_unfolding,[],[f3745,f3091,f3091,f3091]) ).

fof(f4816,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0))) ),
    inference(definition_unfolding,[],[f3748,f3091,f3091,f3091]) ).

fof(f4818,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f3751,f3091]) ).

fof(f4819,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(definition_unfolding,[],[f3764,f3091]) ).

fof(f4820,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(definition_unfolding,[],[f3763,f3091]) ).

fof(f4821,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3762,f3091,f3091]) ).

fof(f4822,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f3761,f3091]) ).

fof(f4823,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(definition_unfolding,[],[f3760,f3091]) ).

fof(f4824,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(definition_unfolding,[],[f3776,f3091]) ).

fof(f4825,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(definition_unfolding,[],[f3775,f3091]) ).

fof(f4826,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(definition_unfolding,[],[f3774,f3091,f3091]) ).

fof(f4827,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(definition_unfolding,[],[f3773,f3091]) ).

fof(f4828,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2)) ),
    inference(definition_unfolding,[],[f3772,f3091]) ).

fof(f4829,plain,
    ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X0)),pls)),
    inference(definition_unfolding,[],[f3778,f3091]) ).

fof(f4830,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1))) ),
    inference(definition_unfolding,[],[f3780,f3091]) ).

fof(f4831,plain,
    ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0))),
    inference(definition_unfolding,[],[f3802,f2913,f2960]) ).

fof(f4832,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(definition_unfolding,[],[f4099,f3091,f2913,f3091]) ).

fof(f4833,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))) ),
    inference(definition_unfolding,[],[f4098,f3091,f2960,f3091]) ).

fof(f4844,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | pls = X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(definition_unfolding,[],[f4119,f3091]) ).

fof(f4845,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | pls = X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(definition_unfolding,[],[f4118,f3091]) ).

fof(f4847,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(sK24(X1,X2)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4123,f3091,f3091]) ).

fof(f4848,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | hBOOL(hAPP_int_bool(X1,sK24(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4122,f3091,f3091]) ).

fof(f4849,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | is_int(sK24(X1,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4121,f3091,f3091]) ).

fof(f4850,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(sK25(X1,X2)),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4126,f3091,f3091]) ).

fof(f4851,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | hBOOL(hAPP_int_bool(X1,sK25(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4125,f3091,f3091]) ).

fof(f4852,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | is_int(sK25(X1,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(X1,X3))
      | hBOOL(hAPP_int_bool(X1,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(definition_unfolding,[],[f4124,f3091,f3091]) ).

fof(f4853,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | is_int(sK27(X0,X1)) ),
    inference(definition_unfolding,[],[f4134,f3091]) ).

fof(f4854,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK27(X0,X1))) ),
    inference(definition_unfolding,[],[f4133,f3091,f3091]) ).

fof(f4855,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,X1)),X1)) ),
    inference(definition_unfolding,[],[f4132,f3091]) ).

fof(f4856,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,sK27(X0,X1)),X1)) ),
    inference(definition_unfolding,[],[f4131,f3091]) ).

fof(f4857,plain,
    ! [X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ is_int(X3)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | sK27(X0,X1) = X3 ),
    inference(definition_unfolding,[],[f4130,f3091,f3091]) ).

fof(f4858,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | one_one_int = zfact(X0) ),
    inference(definition_unfolding,[],[f4138,f3091]) ).

fof(f4859,plain,
    ! [X0] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | zfact(X0) = hAPP_int_int(times_times_int(X0),zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))) ),
    inference(definition_unfolding,[],[f4137,f3091]) ).

fof(f4860,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | inv(X1,inv(X1,X0)) = X0 ),
    inference(definition_unfolding,[],[f4139,f3091,f2960,f2913,f2960]) ).

fof(f4861,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ),
    inference(definition_unfolding,[],[f4140,f3091,f3091,f2913,f2960]) ).

fof(f4862,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hBOOL(hAPP_int_bool(zcong(multInv(X2,X0),multInv(X2,X1)),X2)) ),
    inference(definition_unfolding,[],[f4148,f2913,f2960]) ).

fof(f4863,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | pls != inv(X1,X0) ),
    inference(definition_unfolding,[],[f4149,f3091]) ).

fof(f4864,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X3,X1)),hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3)) ),
    inference(definition_unfolding,[],[f4150,f2913,f2960]) ).

fof(f4865,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X2,X1),multInv(X2,X0)),X2))
      | hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
    inference(definition_unfolding,[],[f4151,f3091,f3091,f2913,f2960]) ).

fof(f4866,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),X0),X1)) ),
    inference(definition_unfolding,[],[f4152,f3091,f2913,f2960]) ).

fof(f4867,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X1,X0),pls),X1)) ),
    inference(definition_unfolding,[],[f4153,f3091,f3091,f2913,f2960]) ).

fof(f4868,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1)) ),
    inference(definition_unfolding,[],[f4154,f3091]) ).

fof(f4869,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X2)),X2)),X0),hAPP_int_int(times_times_int(multInv(X3,X2)),X1)),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X3)) ),
    inference(definition_unfolding,[],[f4155,f3091,f2913,f2960]) ).

fof(f4870,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X3,X2))),X2)),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X2),X1),X3)) ),
    inference(definition_unfolding,[],[f4156,f3091,f2913,f2960]) ).

fof(f4871,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X0),multInv(X3,X2))),X3))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X0),multInv(X3,X1))),X3)) ),
    inference(definition_unfolding,[],[f4157,f3091,f3091,f2913,f2960]) ).

fof(f4872,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X3))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),multInv(X3,X0)),hAPP_int_int(times_times_int(X2),multInv(X3,X1))),X3))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X3)) ),
    inference(definition_unfolding,[],[f4158,f3091,f3091,f3091,f2913,f2960]) ).

fof(f4873,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0))),X0),X1)) ),
    inference(definition_unfolding,[],[f4159,f3091,f2913,f2960]) ).

fof(f4874,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(multInv(X1,multInv(X1,X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),multInv(X1,X0))),multInv(X1,multInv(X1,X0)))),X1)) ),
    inference(definition_unfolding,[],[f4160,f3091,f2913,f2960]) ).

fof(f4876,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X0)),one_one_int),X1)) ),
    inference(definition_unfolding,[],[f4162,f3091,f2913,f2960]) ).

fof(f4877,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(X0,wset(X1,X2)))
      | hBOOL(member_int(inv(X2,X0),wset(X1,X2))) ),
    inference(definition_unfolding,[],[f4163,f2960,f2913,f2960]) ).

fof(f4878,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X2),one_one_int)))
      | ~ hBOOL(member_int(inv(X2,X0),wset(X1,X2)))
      | hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(definition_unfolding,[],[f4164,f2960,f2913,f2960]) ).

fof(f4879,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0) ),
    inference(definition_unfolding,[],[f4192,f2913,f2960,f2913,f2960]) ).

fof(f4880,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))),one_one_int) ),
    inference(definition_unfolding,[],[f4227,f2913,f2960,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4881,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1)))),one_one_int) ),
    inference(definition_unfolding,[],[f4229,f2960,f2913,f2913,f2960,f3091]) ).

fof(f4882,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) ),
    inference(definition_unfolding,[],[f4228,f2960,f2913,f2913,f2960,f3091]) ).

fof(f4883,plain,
    ! [X0,X1] :
      ( pls != hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(definition_unfolding,[],[f4231,f3091]) ).

fof(f4884,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | pls = hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)) ),
    inference(definition_unfolding,[],[f4230,f3091]) ).

fof(f4887,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0))) ),
    inference(definition_unfolding,[],[f4234,f3091,f3091,f3091]) ).

fof(f4888,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),X1)) ),
    inference(definition_unfolding,[],[f4235,f3091]) ).

fof(f4889,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X0)
      | hAPP_int_int(times_times_int(X1),X2) != X0
      | ~ is_int(X2)
      | pls = hAPP_int_int(div_mod_int(X0),X1) ),
    inference(definition_unfolding,[],[f4238,f3091]) ).

fof(f4890,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | pls != hAPP_int_int(div_mod_int(X0),X1)
      | is_int(sK37(X0,X1)) ),
    inference(definition_unfolding,[],[f4237,f3091]) ).

fof(f4891,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | pls != hAPP_int_int(div_mod_int(X0),X1)
      | hAPP_int_int(times_times_int(X1),sK37(X0,X1)) = X0 ),
    inference(definition_unfolding,[],[f4236,f3091]) ).

fof(f4892,plain,
    ! [X0] : pls = hAPP_int_int(div_mod_int(X0),X0),
    inference(definition_unfolding,[],[f4250,f3091]) ).

fof(f4893,plain,
    ! [X0] : pls = hAPP_int_int(div_mod_int(pls),X0),
    inference(definition_unfolding,[],[f4251,f3091,f3091]) ).

fof(f4894,plain,
    ! [X0] : pls = hAPP_int_int(div_mod_int(X0),number_number_of_int(min)),
    inference(definition_unfolding,[],[f4254,f3091]) ).

fof(f4895,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X1))
      | hAPP_int_int(div_mod_int(X0),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X0),X1)),X2) ),
    inference(definition_unfolding,[],[f4255,f3091]) ).

fof(f4901,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(definition_unfolding,[],[f4261,f3091]) ).

fof(f4903,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),pls)) ),
    inference(definition_unfolding,[],[f4264,f3091,f3091]) ).

fof(f4904,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(definition_unfolding,[],[f4263,f3091]) ).

fof(f4905,plain,
    ! [X0,X1] :
      ( ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hAPP_int_int(div_mod_int(X1),X0) = X1 ),
    inference(definition_unfolding,[],[f4265,f3091]) ).

fof(f4906,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X0)),pls))
      | hAPP_int_int(plus_plus_int(X1),X0) = hAPP_int_int(div_mod_int(X1),X0) ),
    inference(definition_unfolding,[],[f4266,f3091,f3091]) ).

fof(f4907,plain,
    ! [X0,X1] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1))) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))),
    inference(definition_unfolding,[],[f4267,f2913,f2960,f2913,f2913]) ).

fof(f4908,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK39(X0,X1,X2)))
      | sP3(X0,X1,X2) ),
    inference(definition_unfolding,[],[f4274,f3091]) ).

fof(f4909,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | sP3(X0,X1,X2) ),
    inference(definition_unfolding,[],[f4269,f3091]) ).

fof(f4910,plain,
    ! [X2,X0,X1,X6,X5] :
      ( ~ sP3(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(definition_unfolding,[],[f4268,f3091,f3091]) ).

fof(f4914,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ sP2(X0,X2,X1)
      | ~ sP3(X0,X2,X1)
      | pls = X2
      | hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(definition_unfolding,[],[f4287,f3091]) ).

fof(f4915,plain,
    ! [X2,X0,X1] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      | pls != X2
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(definition_unfolding,[],[f4286,f3091]) ).

fof(f4916,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(definition_unfolding,[],[f4289,f3091,f3091,f3091]) ).

fof(f4917,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),hAPP_int_int(times_times_int(X1),X3))) ),
    inference(definition_unfolding,[],[f4290,f3091,f3091]) ).

fof(f4918,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2))) ),
    inference(definition_unfolding,[],[f4291,f3091,f3091]) ).

fof(f4919,plain,
    ! [X2,X3,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X0),X3))),X2)),pls)) ),
    inference(definition_unfolding,[],[f4292,f3091,f3091,f3091]) ).

fof(f4921,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | pls = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(definition_unfolding,[],[f4295,f3091,f3091,f3091]) ).

fof(f4922,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3) != X0
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | pls = X1
      | hAPP_int_int(div_mod_int(X0),X1) = X3 ),
    inference(definition_unfolding,[],[f4294,f3091,f3091,f3091]) ).

fof(f4924,plain,
    ! [X0] :
      ( one_one_int != hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))
      | pls != hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ),
    inference(definition_unfolding,[],[f4298,f3091,f2913,f2960,f2913,f2960]) ).

fof(f4925,plain,
    ! [X0] :
      ( pls = hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))
      | one_one_int = hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ),
    inference(definition_unfolding,[],[f4297,f2913,f2960,f3091,f2913,f2960]) ).

fof(f4926,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hAPP_int_int(minus_minus_int(X0),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) ),
    inference(definition_unfolding,[],[f4299,f3091]) ).

fof(f4927,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(definition_unfolding,[],[f4300,f2913,f2960,f2913,f2960,f2913,f2960,f3091]) ).

fof(f4928,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | pls != hAPP_int_int(div_mod_int(X0),X1)
      | is_int(sK42(X0,X1)) ),
    inference(definition_unfolding,[],[f4302,f3091]) ).

fof(f4929,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | pls != hAPP_int_int(div_mod_int(X0),X1)
      | hAPP_int_int(times_times_int(X1),sK42(X0,X1)) = X0 ),
    inference(definition_unfolding,[],[f4301,f3091]) ).

fof(f4930,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X2))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X0),X2)),hAPP_int_int(div_mod_int(X1),X2)),hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(definition_unfolding,[],[f4303,f4313,f4313,f2913,f2960]) ).

fof(f4933,plain,
    ! [X0,X1] :
      ( pls = hAPP_int_int(div_mod_int(X0),X1)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(definition_unfolding,[],[f4321,f3091,f3091,f4313]) ).

fof(f4934,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | pls != hAPP_int_int(div_mod_int(X0),X1) ),
    inference(definition_unfolding,[],[f4320,f3091,f4313,f3091]) ).

fof(f4935,plain,
    ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(div_mod_int(X0),X1)),X1)),
    inference(definition_unfolding,[],[f4322,f4313]) ).

fof(f4936,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(X0),X1)),X1)) ),
    inference(definition_unfolding,[],[f4323,f4313,f3091]) ).

fof(f4937,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ hBOOL(member_int(X0,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),cOMBC_int_int_bool(ord_less_int,X1)))))
      | hAPP_int_int(div_mod_int(X0),X1) = X0 ),
    inference(definition_unfolding,[],[f4324,f4313,f4348]) ).

fof(f4938,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X0),X1))) ),
    inference(definition_unfolding,[],[f4338,f3091,f4313,f3091]) ).

fof(f4939,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | hAPP_int_int(div_mod_int(X0),X2) = hAPP_int_int(div_mod_int(X1),X2) ),
    inference(definition_unfolding,[],[f4340,f4313,f4313,f3091]) ).

fof(f4941,plain,
    ! [X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(definition_unfolding,[],[f4347,f2913,f2960,f2913,f2960,f2913,f2913,f2960]) ).

fof(f4979,plain,
    ! [X0] : hAPP_real_real(plus_plus_real(X0),zero_zero_real) = X0,
    inference(equality_resolution,[],[f3086]) ).

fof(f4986,plain,
    ! [X3,X0,X1,X4] :
      ( ~ is_int(X4)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | pls = X4
      | X0 = X1
      | hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X1)) != hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X4),X0)) ),
    inference(equality_resolution,[],[f4564]) ).

fof(f4987,plain,
    ! [X3,X0,X1,X4] :
      ( zero_zero_nat = X4
      | X0 = X1
      | hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X1)) != hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(times_times_nat(X4),X0)) ),
    inference(equality_resolution,[],[f3129]) ).

fof(f4988,plain,
    ! [X3,X0,X1,X4] :
      ( zero_zero_real = X4
      | X0 = X1
      | hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X1)) != hAPP_real_real(plus_plus_real(X3),hAPP_real_real(times_times_real(X4),X0)) ),
    inference(equality_resolution,[],[f3130]) ).

fof(f5018,plain,
    ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),zero_zero_nat))),
    inference(equality_resolution,[],[f3312]) ).

fof(f5020,plain,
    ( ~ is_int(min)
    | min = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),min)),min) ),
    inference(equality_resolution,[],[f4665]) ).

fof(f5034,plain,
    ! [X2,X3,X0] :
      ( ~ is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3)))
      | ~ is_int(X3)
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),X3))),X2)) ),
    inference(equality_resolution,[],[f3427]) ).

fof(f5035,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),X1) = X0 ),
    inference(equality_resolution,[],[f3451]) ).

fof(f5036,plain,
    ! [X2,X3,X0,X4] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X2,X3),X4))
      | ~ hBOOL(hAPP_int_bool(zcong(X3,X0),X4))
      | hBOOL(hAPP_int_bool(zcong(X2,X0),X4)) ),
    inference(equality_resolution,[],[f3482]) ).

fof(f5040,plain,
    ! [X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)),
    inference(equality_resolution,[],[f3543]) ).

fof(f5056,plain,
    ! [X1] :
      ( zero_zero_nat = X1
      | zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) ),
    inference(equality_resolution,[],[f3641]) ).

fof(f5061,plain,
    ! [X1] : one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X1),
    inference(equality_resolution,[],[f3800]) ).

fof(f5062,plain,
    ! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat),
    inference(equality_resolution,[],[f3799]) ).

fof(f5063,plain,
    ! [X2,X3,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3))) ),
    inference(equality_resolution,[],[f3801]) ).

fof(f5064,plain,
    ! [X3,X1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X3),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
      | sK17(hAPP_nat_real(power_power_real(X3),X1),X1) = X3 ),
    inference(equality_resolution,[],[f3805]) ).

fof(f5085,plain,
    ! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X1)),
    inference(equality_resolution,[],[f3887]) ).

fof(f5095,plain,
    ! [X1] : zero_zero_nat = hAPP_nat_nat(times_times_nat(zero_zero_nat),X1),
    inference(equality_resolution,[],[f3948]) ).

fof(f5096,plain,
    ! [X0] : zero_zero_nat = hAPP_nat_nat(times_times_nat(X0),zero_zero_nat),
    inference(equality_resolution,[],[f3947]) ).

fof(f5101,plain,
    ! [X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
    inference(equality_resolution,[],[f3968]) ).

fof(f5103,plain,
    ! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
    inference(equality_resolution,[],[f3976]) ).

fof(f5104,plain,
    ! [X2,X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X2))),
    inference(equality_resolution,[],[f3988]) ).

fof(f5119,plain,
    ! [X2,X3,X0,X4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X4),X0)),X2) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X0)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X4),X3)),X0)),X2)) ),
    inference(equality_resolution,[],[f4095]) ).

fof(f5120,plain,
    ! [X2,X1] :
      ( ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)))
      | ~ is_int(X2)
      | ~ is_int(X1)
      | hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,twoSqu1241645765sum2sq(product_Pair_int_int(X1,X2)))) ),
    inference(equality_resolution,[],[f4103]) ).

fof(f5125,plain,
    ! [X2,X1] :
      ( ~ is_int(hAPP_int_int(times_times_int(X1),X2))
      | ~ is_int(X2)
      | pls = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),X2)),X1) ),
    inference(equality_resolution,[],[f4889]) ).

fof(f5126,plain,
    ! [X0,X1,X6,X5] :
      ( ~ sP3(X0,X1,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(equality_resolution,[],[f4910]) ).

fof(f5128,plain,
    ! [X0,X1] :
      ( ~ is_int(pls)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),pls)))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(equality_resolution,[],[f4915]) ).

fof(f5130,plain,
    ! [X2,X3,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | pls = X1
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3)),X1) = X3 ),
    inference(equality_resolution,[],[f4921]) ).

fof(f5131,plain,
    ! [X2,X3,X1] :
      ( ~ is_int(X3)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | pls = X1
      | hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3)),X1) = X3 ),
    inference(equality_resolution,[],[f4922]) ).

fof(f5133,plain,
    ! [X2,X1] : zero_zero_nat = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X1),
    inference(equality_resolution,[],[f4307]) ).

tcf(c_49,plain,
    is_int(one_one_int),
    inference(cnf_transformation,[],[f2606]) ).

tcf(c_51,plain,
    is_int(undefined_int(int)),
    inference(cnf_transformation,[],[f2608]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(multInv(X0,X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2609]) ).

tcf(c_53,plain,
    ! [X0: $i] :
      ( is_int(zfact(X0))
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2610]) ).

tcf(c_56,plain,
    is_int(min),
    inference(cnf_transformation,[],[f2613]) ).

tcf(c_57,plain,
    is_int(pls),
    inference(cnf_transformation,[],[f2614]) ).

tcf(c_58,plain,
    ! [X0: $i] :
      ( is_int(number_number_of_int(X0))
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2615]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(legendre(X0,X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2616]) ).

tcf(c_61,plain,
    ! [X0: $i] : is_int(twoSqu1241645765sum2sq(X0)),
    inference(cnf_transformation,[],[f2618]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(inv(X0,X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2619]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(X1,X0))
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2622]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_nat_int(X0,X1)),
    inference(cnf_transformation,[],[f2624]) ).

tcf(c_70,plain,
    is_int(m),
    inference(cnf_transformation,[],[f2627]) ).

tcf(c_71,plain,
    is_int(s1),
    inference(cnf_transformation,[],[f2628]) ).

tcf(c_72,plain,
    is_int(s),
    inference(cnf_transformation,[],[f2629]) ).

tcf(c_73,plain,
    is_int(t),
    inference(cnf_transformation,[],[f2630]) ).

tcf(c_74,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    inference(cnf_transformation,[],[f2631]) ).

tcf(c_77,plain,
    ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) )
    | ( one_one_int != t ) ),
    inference(cnf_transformation,[],[f4353]) ).

tcf(c_80,plain,
    ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) )
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(cnf_transformation,[],[f4354]) ).

tcf(c_81,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4355]) ).

tcf(c_82,plain,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4356]) ).

tcf(c_83,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int),
    inference(cnf_transformation,[],[f4357]) ).

tcf(c_84,plain,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t))),
    inference(cnf_transformation,[],[f4358]) ).

tcf(c_86,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4360]) ).

tcf(c_87,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4361]) ).

tcf(c_88,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4362]) ).

tcf(c_89,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)) = hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4363]) ).

tcf(c_93,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4367]) ).

tcf(c_97,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(times_times_int(X0),X0),
    inference(cnf_transformation,[],[f4371]) ).

tcf(c_98,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_real_real(times_times_real(X0),X0),
    inference(cnf_transformation,[],[f4372]) ).

tcf(c_99,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_nat(times_times_nat(X0),X0),
    inference(cnf_transformation,[],[f4373]) ).

tcf(c_103,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X1)),
    inference(cnf_transformation,[],[f4377]) ).

tcf(c_104,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X1)),
    inference(cnf_transformation,[],[f4378]) ).

tcf(c_105,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X1)),
    inference(cnf_transformation,[],[f4379]) ).

tcf(c_106,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)),
    inference(cnf_transformation,[],[f4380]) ).

tcf(c_107,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(cnf_transformation,[],[f4381]) ).

tcf(c_108,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int),
    inference(cnf_transformation,[],[f4382]) ).

tcf(c_109,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real),
    inference(cnf_transformation,[],[f4383]) ).

tcf(c_112,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),sK9) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int),
    inference(cnf_transformation,[],[f4386]) ).

tcf(c_113,plain,
    is_int(sK9),
    inference(cnf_transformation,[],[f2669]) ).

tcf(c_114,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
    inference(cnf_transformation,[],[f2671]) ).

tcf(c_115,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2672]) ).

tcf(c_118,plain,
    ! [X0: $i] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X0)) ),
    inference(cnf_transformation,[],[f5138]) ).

tcf(c_120,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2677]) ).

tcf(c_121,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2678]) ).

tcf(c_122,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f2679]) ).

tcf(c_123,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f2680]) ).

tcf(c_124,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f2681]) ).

tcf(c_131,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2689]) ).

tcf(c_132,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f2688]) ).

tcf(c_133,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2691]) ).

tcf(c_134,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2690]) ).

tcf(c_137,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2695]) ).

tcf(c_138,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2694]) ).

tcf(c_141,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2699]) ).

tcf(c_142,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(cnf_transformation,[],[f2698]) ).

tcf(c_143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X3),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2700]) ).

tcf(c_144,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f2701]) ).

tcf(c_145,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f2702]) ).

tcf(c_146,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f2703]) ).

tcf(c_149,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_nat(plus_plus_nat(X0),X0),
    inference(cnf_transformation,[],[f4388]) ).

tcf(c_150,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
    inference(cnf_transformation,[],[f4389]) ).

tcf(c_153,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4392]) ).

tcf(c_154,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(cnf_transformation,[],[f4393]) ).

tcf(c_157,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4396]) ).

tcf(c_158,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(cnf_transformation,[],[f4397]) ).

tcf(c_162,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4400]) ).

tcf(c_163,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(cnf_transformation,[],[f4401]) ).

tcf(c_167,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4404]) ).

tcf(c_168,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(cnf_transformation,[],[f4405]) ).

tcf(c_169,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2727]) ).

tcf(c_170,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2726]) ).

tcf(c_171,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2729]) ).

tcf(c_172,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2728]) ).

tcf(c_173,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X2)),hAPP_int_int(plus_plus_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2730]) ).

tcf(c_174,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2731]) ).

tcf(c_175,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2734]) ).

tcf(c_176,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2733]) ).

tcf(c_177,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X0),X1)) ) ),
    inference(cnf_transformation,[],[f2732]) ).

tcf(c_178,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)) = one_one_nat,
    inference(cnf_transformation,[],[f4406]) ).

tcf(c_180,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4408]) ).

tcf(c_181,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(cnf_transformation,[],[f4409]) ).

tcf(c_182,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4410]) ).

tcf(c_183,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(cnf_transformation,[],[f4411]) ).

tcf(c_186,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4414]) ).

tcf(c_187,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(cnf_transformation,[],[f4415]) ).

tcf(c_190,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4418]) ).

tcf(c_191,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(cnf_transformation,[],[f4419]) ).

tcf(c_193,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2751]) ).

tcf(c_194,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),one_one_int)),X1)) ),
    inference(cnf_transformation,[],[f2750]) ).

tcf(c_195,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2753]) ).

tcf(c_196,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f2752]) ).

tcf(c_197,plain,
    hBOOL(hAPP_int_bool(zprime,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(cnf_transformation,[],[f4420]) ).

tcf(c_198,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(cnf_transformation,[],[f2755]) ).

tcf(c_211,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f2768]) ).

tcf(c_212,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f2769]) ).

tcf(c_213,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    inference(cnf_transformation,[],[f2770]) ).

tcf(c_217,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)),
    inference(cnf_transformation,[],[f2774]) ).

tcf(c_218,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(cnf_transformation,[],[f2775]) ).

tcf(c_219,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X2)),
    inference(cnf_transformation,[],[f2776]) ).

tcf(c_220,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0),
    inference(cnf_transformation,[],[f2777]) ).

tcf(c_221,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    inference(cnf_transformation,[],[f2778]) ).

tcf(c_222,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    inference(cnf_transformation,[],[f2779]) ).

tcf(c_226,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X1,X0))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2784]) ).

tcf(c_227,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ~ hBOOL(member_int(X0,X1)) ),
    inference(cnf_transformation,[],[f2783]) ).

tcf(c_228,plain,
    ! [X0: $i] : collect_int(X0) = X0,
    inference(cnf_transformation,[],[f2785]) ).

tcf(c_232,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f2789]) ).

tcf(c_233,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f2790]) ).

tcf(c_234,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    inference(cnf_transformation,[],[f2791]) ).

tcf(c_237,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    inference(cnf_transformation,[],[f2794]) ).

tcf(c_238,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    inference(cnf_transformation,[],[f2795]) ).

tcf(c_240,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X2)),
    inference(cnf_transformation,[],[f2797]) ).

tcf(c_241,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    inference(cnf_transformation,[],[f2798]) ).

tcf(c_242,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(cnf_transformation,[],[f2799]) ).

tcf(c_243,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0),
    inference(cnf_transformation,[],[f2800]) ).

tcf(c_245,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != number_number_of_int(X1) ) ),
    inference(cnf_transformation,[],[f2801]) ).

tcf(c_247,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( number267125858f_real(X0) != number267125858f_real(X1) ) ),
    inference(cnf_transformation,[],[f2803]) ).

tcf(c_249,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) ) ),
    inference(cnf_transformation,[],[f4422]) ).

tcf(c_251,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(X1),X1) ) ),
    inference(cnf_transformation,[],[f4424]) ).

tcf(c_252,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),
    inference(cnf_transformation,[],[f2815]) ).

tcf(c_253,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0),
    inference(cnf_transformation,[],[f2816]) ).

tcf(c_254,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(X0) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2817]) ).

tcf(c_255,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f2818]) ).

tcf(c_256,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    inference(cnf_transformation,[],[f2819]) ).

tcf(c_257,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
    inference(cnf_transformation,[],[f2820]) ).

tcf(c_262,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4429]) ).

tcf(c_263,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(cnf_transformation,[],[f4430]) ).

tcf(c_266,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4433]) ).

tcf(c_267,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(cnf_transformation,[],[f4434]) ).

tcf(c_268,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4435]) ).

tcf(c_269,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(cnf_transformation,[],[f4436]) ).

tcf(c_272,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4439]) ).

tcf(c_273,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(cnf_transformation,[],[f4440]) ).

tcf(c_274,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4441]) ).

tcf(c_275,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(cnf_transformation,[],[f4442]) ).

tcf(c_276,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4443]) ).

tcf(c_277,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(cnf_transformation,[],[f4444]) ).

tcf(c_279,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int)))
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f5143]) ).

tcf(c_281,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(cnf_transformation,[],[f4445]) ).

tcf(c_282,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(cnf_transformation,[],[f4446]) ).

tcf(c_283,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)),
    inference(cnf_transformation,[],[f4447]) ).

tcf(c_284,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(cnf_transformation,[],[f4448]) ).

tcf(c_285,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f4449]) ).

tcf(c_286,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(cnf_transformation,[],[f4450]) ).

tcf(c_287,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(cnf_transformation,[],[f4451]) ).

tcf(c_288,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(cnf_transformation,[],[f4452]) ).

tcf(c_289,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4453]) ).

tcf(c_290,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(cnf_transformation,[],[f4454]) ).

tcf(c_291,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f4455]) ).

tcf(c_292,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(cnf_transformation,[],[f4456]) ).

tcf(c_293,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f4457]) ).

tcf(c_294,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(cnf_transformation,[],[f4458]) ).

tcf(c_295,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(cnf_transformation,[],[f4459]) ).

tcf(c_296,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(cnf_transformation,[],[f4460]) ).

tcf(c_297,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4461]) ).

tcf(c_298,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(cnf_transformation,[],[f4462]) ).

tcf(c_299,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f4463]) ).

tcf(c_315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( X0 = X2 )
      | ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X2),X1)) ) ),
    inference(cnf_transformation,[],[f2878]) ).

tcf(c_317,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( X0 = X2 )
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X3)),hAPP_nat_nat(times_times_nat(X2),X1)) ) ),
    inference(cnf_transformation,[],[f2881]) ).

tcf(c_319,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( X0 = X2 )
      | ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X3)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X3)),hAPP_real_real(times_times_real(X2),X1)) ) ),
    inference(cnf_transformation,[],[f2884]) ).

tcf(c_320,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f2887]) ).

tcf(c_322,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2)) = hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),X2)),
    inference(cnf_transformation,[],[f2889]) ).

tcf(c_325,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(X0),one_one_real) = X0,
    inference(cnf_transformation,[],[f2892]) ).

tcf(c_332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != pls,
    inference(cnf_transformation,[],[f4464]) ).

tcf(c_334,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(cnf_transformation,[],[f4466]) ).

tcf(c_340,plain,
    hAPP_int_int(plus_plus_int(pls),pls) = pls,
    inference(cnf_transformation,[],[f4472]) ).

tcf(c_346,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),one_one_int) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2914]) ).

tcf(c_347,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),X0) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f2915]) ).

tcf(c_348,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),
    inference(cnf_transformation,[],[f2916]) ).

tcf(c_350,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(cnf_transformation,[],[f2918]) ).

tcf(c_351,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f2919]) ).

tcf(c_353,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(times_times_int(X1),X0)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2921]) ).

tcf(c_356,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X0)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f2924]) ).

tcf(c_358,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(cnf_transformation,[],[f4475]) ).

tcf(c_368,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0),
    inference(cnf_transformation,[],[f2936]) ).

tcf(c_369,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X0)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)),X0),
    inference(cnf_transformation,[],[f2937]) ).

tcf(c_370,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),X0),
    inference(cnf_transformation,[],[f2938]) ).

tcf(c_371,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(cnf_transformation,[],[f2939]) ).

tcf(c_372,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0) = hAPP_nat_nat(plus_plus_nat(X0),X0),
    inference(cnf_transformation,[],[f2940]) ).

tcf(c_373,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0) = hAPP_real_real(plus_plus_real(X0),X0),
    inference(cnf_transformation,[],[f2941]) ).

tcf(c_378,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),X2)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f2946]) ).

tcf(c_379,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(number267125858f_real(X1)),X2)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f2947]) ).

tcf(c_382,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),
    inference(cnf_transformation,[],[f2950]) ).

tcf(c_383,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(times_times_int(X0),X1)),
    inference(cnf_transformation,[],[f2951]) ).

tcf(c_384,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f2952]) ).

tcf(c_385,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(plus_plus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f2953]) ).

tcf(c_387,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f2955]) ).

tcf(c_388,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f2956]) ).

tcf(c_389,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)),
    inference(cnf_transformation,[],[f2957]) ).

tcf(c_391,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X1))),hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),
    inference(cnf_transformation,[],[f4477]) ).

tcf(c_392,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(cnf_transformation,[],[f4478]) ).

tcf(c_393,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0))),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(cnf_transformation,[],[f4479]) ).

tcf(c_398,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)) = one_one_int,
    inference(cnf_transformation,[],[f4484]) ).

tcf(c_400,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)) = one_one_real,
    inference(cnf_transformation,[],[f4486]) ).

tcf(c_406,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X1))),X1) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),X1),
    inference(cnf_transformation,[],[f4492]) ).

tcf(c_407,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(cnf_transformation,[],[f4493]) ).

tcf(c_408,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(cnf_transformation,[],[f4494]) ).

tcf(c_409,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),X0),
    inference(cnf_transformation,[],[f4495]) ).

tcf(c_410,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),X0),
    inference(cnf_transformation,[],[f4496]) ).

tcf(c_411,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X0)),X0),
    inference(cnf_transformation,[],[f4497]) ).

tcf(c_412,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(cnf_transformation,[],[f4498]) ).

tcf(c_418,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(cnf_transformation,[],[f4504]) ).

tcf(c_420,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(X0),number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = hAPP_real_real(plus_plus_real(X0),X0),
    inference(cnf_transformation,[],[f4506]) ).

tcf(c_426,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4512]) ).

tcf(c_427,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int))),
    inference(cnf_transformation,[],[f4513]) ).

tcf(c_428,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0))
      | ( number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = X0 )
      | ( number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f4514]) ).

tcf(c_429,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(cnf_transformation,[],[f4515]) ).

tcf(c_431,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4517]) ).

tcf(c_432,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3001]) ).

tcf(c_433,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0)) ),
    inference(cnf_transformation,[],[f3002]) ).

tcf(c_434,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_real_real(times_times_real(X0),hAPP_nat_real(power_power_real(X0),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0)) ),
    inference(cnf_transformation,[],[f3003]) ).

tcf(c_435,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3004]) ).

tcf(c_436,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0)) ),
    inference(cnf_transformation,[],[f3005]) ).

tcf(c_437,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(X0),hAPP_nat_real(power_power_real(X0),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0)) ),
    inference(cnf_transformation,[],[f3006]) ).

tcf(c_441,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3011]) ).

tcf(c_442,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(cnf_transformation,[],[f3010]) ).

tcf(c_443,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3013]) ).

tcf(c_444,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3012]) ).

tcf(c_445,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3015]) ).

tcf(c_446,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3014]) ).

tcf(c_447,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(s1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4518]) ).

tcf(c_448,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)),
    inference(cnf_transformation,[],[f4519]) ).

tcf(c_449,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4520]) ).

tcf(c_450,plain,
    hBOOL(hAPP_int_bool(zcong(s1,s),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4521]) ).

tcf(c_451,plain,
    is_int(sK10),
    inference(cnf_transformation,[],[f3024]) ).

tcf(c_452,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK10)),
    inference(cnf_transformation,[],[f4522]) ).

tcf(c_453,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4523]) ).

tcf(c_454,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK10),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4524]) ).

tcf(c_455,plain,
    ! [X0: $i] :
      ( ( X0 = sK10 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))) ),
    inference(cnf_transformation,[],[f4525]) ).

tcf(c_456,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK11)),
    inference(cnf_transformation,[],[f4526]) ).

tcf(c_457,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4527]) ).

tcf(c_458,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK11),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4528]) ).

tcf(c_459,plain,
    is_int(sK11),
    inference(cnf_transformation,[],[f3025]) ).

tcf(c_460,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4529]) ).

tcf(c_470,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3039]) ).

tcf(c_471,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3040]) ).

tcf(c_472,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3041]) ).

tcf(c_473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X3),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3042]) ).

tcf(c_474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3043]) ).

tcf(c_475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X3),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3044]) ).

tcf(c_476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X3)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3045]) ).

tcf(c_477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X3)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3046]) ).

tcf(c_478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X3)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3047]) ).

tcf(c_479,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ is_int(X2)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ( hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X2),X1) ) ),
    inference(cnf_transformation,[],[f4533]) ).

tcf(c_480,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1) ) ),
    inference(cnf_transformation,[],[f3049]) ).

tcf(c_481,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hAPP_nat_real(power_power_real(X0),X1) != hAPP_nat_real(power_power_real(X2),X1) ) ),
    inference(cnf_transformation,[],[f3050]) ).

tcf(c_482,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4534]) ).

tcf(c_483,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4535]) ).

tcf(c_485,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3054]) ).

tcf(c_486,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3055]) ).

tcf(c_488,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( hAPP_nat_int(power_power_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4537]) ).

tcf(c_489,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_nat_real(power_power_real(X0),X1) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3058]) ).

tcf(c_491,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_int(power_power_int(pls),X0) = pls ) ),
    inference(cnf_transformation,[],[f4539]) ).

tcf(c_495,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_real(power_power_real(zero_zero_real),X0) = zero_zero_real ) ),
    inference(cnf_transformation,[],[f3063]) ).

tcf(c_497,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4541]) ).

tcf(c_498,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3067]) ).

tcf(c_499,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3068]) ).

tcf(c_508,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0,
    inference(cnf_transformation,[],[f3077]) ).

tcf(c_513,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f4547]) ).

tcf(c_516,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(X0),zero_zero_real) = X0,
    inference(cnf_transformation,[],[f4979]) ).

tcf(c_517,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3085]) ).

tcf(c_519,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(X0),X0) != pls ) ),
    inference(cnf_transformation,[],[f4549]) ).

tcf(c_521,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),X0) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3089]) ).

tcf(c_523,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),X0) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4551]) ).

tcf(c_524,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),pls) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4552]) ).

tcf(c_527,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f3097]) ).

tcf(c_528,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X2)),hAPP_nat_int(power_power_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4554]) ).

tcf(c_529,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3099]) ).

tcf(c_530,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),X2)),hAPP_nat_real(power_power_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3100]) ).

tcf(c_531,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4555]) ).

tcf(c_533,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f3103]) ).

tcf(c_534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X3)),one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),X1),one_one_int),X2)) ),
    inference(cnf_transformation,[],[f3104]) ).

tcf(c_535,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3106]) ).

tcf(c_536,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X0),X2)))) ),
    inference(cnf_transformation,[],[f3105]) ).

tcf(c_537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X2),X3))),X4))) ),
    inference(cnf_transformation,[],[f3108]) ).

tcf(c_538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X4),X3))),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X2))) ),
    inference(cnf_transformation,[],[f3107]) ).

tcf(c_539,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1))) ),
    inference(cnf_transformation,[],[f4556]) ).

tcf(c_540,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f3110]) ).

tcf(c_541,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3111]) ).

tcf(c_542,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X1)),hAPP_nat_int(power_power_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),one_one_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4557]) ).

tcf(c_543,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X1)),hAPP_nat_nat(power_power_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3113]) ).

tcf(c_544,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X1)),hAPP_nat_real(power_power_real(X2),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),one_one_real))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3114]) ).

tcf(c_545,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X1)),hAPP_nat_int(power_power_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),one_one_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4558]) ).

tcf(c_546,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X1)),hAPP_nat_nat(power_power_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3116]) ).

tcf(c_547,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X1)),hAPP_nat_real(power_power_real(X2),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),one_one_real))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3117]) ).

tcf(c_550,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3121]) ).

tcf(c_551,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3120]) ).

tcf(c_553,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) != pls ) ),
    inference(cnf_transformation,[],[f4562]) ).

tcf(c_554,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) != pls ) ),
    inference(cnf_transformation,[],[f4563]) ).

tcf(c_558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X2 = X3 )
      | ( X1 = pls )
      | ~ is_int(X3)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X2)) != hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X3)) ) ),
    inference(cnf_transformation,[],[f4986]) ).

tcf(c_559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X2 = X3 )
      | ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X3)) ) ),
    inference(cnf_transformation,[],[f4987]) ).

tcf(c_560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X2 = X3 )
      | ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X2)) != hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X3)) ) ),
    inference(cnf_transformation,[],[f4988]) ).

tcf(c_561,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2))) ),
    inference(cnf_transformation,[],[f3131]) ).

tcf(c_562,plain,
    number_number_of_int(pls) = pls,
    inference(cnf_transformation,[],[f4565]) ).

tcf(c_568,plain,
    number267125858f_real(pls) = zero_zero_real,
    inference(cnf_transformation,[],[f3138]) ).

tcf(c_571,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(cnf_transformation,[],[f4570]) ).

tcf(c_572,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4571]) ).

tcf(c_573,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(cnf_transformation,[],[f4572]) ).

tcf(c_574,plain,
    number_number_of_int(pls) = pls,
    inference(cnf_transformation,[],[f4573]) ).

tcf(c_575,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
    inference(cnf_transformation,[],[f4574]) ).

tcf(c_576,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f4575]) ).

tcf(c_580,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),X1))),hAPP_nat_nat(power_power_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat)) ),
    inference(cnf_transformation,[],[f3150]) ).

tcf(c_581,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),hAPP_nat_real(power_power_real(X0),X1))),hAPP_nat_real(power_power_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),one_one_real)) ),
    inference(cnf_transformation,[],[f3151]) ).

tcf(c_582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3))) ),
    inference(cnf_transformation,[],[f3152]) ).

tcf(c_583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X3))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3))) ),
    inference(cnf_transformation,[],[f3153]) ).

tcf(c_584,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(cnf_transformation,[],[f4579]) ).

tcf(c_585,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)))),
    inference(cnf_transformation,[],[f3155]) ).

tcf(c_587,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls)) ),
    inference(cnf_transformation,[],[f4581]) ).

tcf(c_588,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls)) ),
    inference(cnf_transformation,[],[f4582]) ).

tcf(c_590,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3160]) ).

tcf(c_591,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3159]) ).

tcf(c_592,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3165]) ).

tcf(c_593,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f3163]) ).

tcf(c_594,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f3162]) ).

tcf(c_595,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls)),
    inference(cnf_transformation,[],[f4583]) ).

tcf(c_596,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    inference(cnf_transformation,[],[f3167]) ).

tcf(c_597,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
      | ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4584]) ).

tcf(c_598,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))))
      | ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4585]) ).

tcf(c_600,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f3173]) ).

tcf(c_601,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X1)),hAPP_real_real(times_times_real(X0),X0))))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f3172]) ).

tcf(c_603,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3176]) ).

tcf(c_604,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3175]) ).

tcf(c_605,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(cnf_transformation,[],[f3174]) ).

tcf(c_606,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),number_number_of_int(X0))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(cnf_transformation,[],[f4587]) ).

tcf(c_608,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f3179]) ).

tcf(c_609,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f3180]) ).

tcf(c_610,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f3181]) ).

tcf(c_611,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4589]) ).

tcf(c_612,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4590]) ).

tcf(c_613,plain,
    ( ( hAPP_int_int(times_times_int(one_one_int),one_one_int) = one_one_int )
    | ~ is_int(one_one_int)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
    inference(cnf_transformation,[],[f5151]) ).

tcf(c_614,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f4592]) ).

tcf(c_615,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_int )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f4593]) ).

tcf(c_616,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4594]) ).

tcf(c_617,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(cnf_transformation,[],[f4595]) ).

tcf(c_618,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4596]) ).

tcf(c_619,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4597]) ).

tcf(c_620,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f3192]) ).

tcf(c_621,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f3191]) ).

tcf(c_622,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4598]) ).

tcf(c_623,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(cnf_transformation,[],[f4599]) ).

tcf(c_624,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3196]) ).

tcf(c_625,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3195]) ).

tcf(c_626,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f3198]) ).

tcf(c_627,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(cnf_transformation,[],[f3197]) ).

tcf(c_628,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4600]) ).

tcf(c_629,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4601]) ).

tcf(c_630,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3202]) ).

tcf(c_631,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3201]) ).

tcf(c_632,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4602]) ).

tcf(c_633,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
    inference(cnf_transformation,[],[f4603]) ).

tcf(c_634,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4604]) ).

tcf(c_642,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(cnf_transformation,[],[f4612]) ).

tcf(c_643,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
    inference(cnf_transformation,[],[f4613]) ).

tcf(c_644,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(cnf_transformation,[],[f4614]) ).

tcf(c_645,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(cnf_transformation,[],[f4615]) ).

tcf(c_646,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(cnf_transformation,[],[f4616]) ).

tcf(c_647,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ) ),
    inference(cnf_transformation,[],[f4617]) ).

tcf(c_648,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
      | ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ) ),
    inference(cnf_transformation,[],[f4618]) ).

tcf(c_649,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ) ),
    inference(cnf_transformation,[],[f4619]) ).

tcf(c_650,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),zero_zero_real)),
    inference(cnf_transformation,[],[f4620]) ).

tcf(c_651,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),pls)),
    inference(cnf_transformation,[],[f4621]) ).

tcf(c_652,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f4622]) ).

tcf(c_654,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ( X0 = pls )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4624]) ).

tcf(c_660,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != pls ) ),
    inference(cnf_transformation,[],[f4630]) ).

tcf(c_661,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != pls ) ),
    inference(cnf_transformation,[],[f4631]) ).

tcf(c_665,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f3236]) ).

tcf(c_666,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X2),X1)) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X2)),X1),
    inference(cnf_transformation,[],[f3237]) ).

tcf(c_667,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f3238]) ).

tcf(c_668,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3239]) ).

tcf(c_669,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3240]) ).

tcf(c_670,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3241]) ).

tcf(c_671,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(one_one_real),X0) = one_one_real,
    inference(cnf_transformation,[],[f3242]) ).

tcf(c_673,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(one_one_int),X0) = one_one_int,
    inference(cnf_transformation,[],[f3244]) ).

tcf(c_674,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),X2) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f3245]) ).

tcf(c_675,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),X2) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f3246]) ).

tcf(c_676,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),X2) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f3247]) ).

tcf(c_680,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
    inference(cnf_transformation,[],[f4635]) ).

tcf(c_681,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
    inference(cnf_transformation,[],[f4636]) ).

tcf(c_683,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)) ),
    inference(cnf_transformation,[],[f4638]) ).

tcf(c_684,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)) ),
    inference(cnf_transformation,[],[f4639]) ).

tcf(c_686,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls)) ),
    inference(cnf_transformation,[],[f4641]) ).

tcf(c_687,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls)) ),
    inference(cnf_transformation,[],[f4642]) ).

tcf(c_688,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)),
    inference(cnf_transformation,[],[f4643]) ).

tcf(c_689,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),pls)),
    inference(cnf_transformation,[],[f4644]) ).

tcf(c_690,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f4645]) ).

tcf(c_691,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f4646]) ).

tcf(c_693,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4648]) ).

tcf(c_694,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f4649]) ).

tcf(c_696,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)))),
    inference(cnf_transformation,[],[f4651]) ).

tcf(c_697,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1)))),
    inference(cnf_transformation,[],[f4652]) ).

tcf(c_698,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0)) ),
    inference(cnf_transformation,[],[f3269]) ).

tcf(c_699,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(cnf_transformation,[],[f3270]) ).

tcf(c_700,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3271]) ).

tcf(c_701,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3272]) ).

tcf(c_702,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3273]) ).

tcf(c_703,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3274]) ).

tcf(c_704,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | ( hAPP_nat_real(power_power_real(X0),X1) != hAPP_nat_real(power_power_real(X0),X2) ) ),
    inference(cnf_transformation,[],[f3275]) ).

tcf(c_705,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X0),X2) ) ),
    inference(cnf_transformation,[],[f3277]) ).

tcf(c_706,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ( hAPP_nat_int(power_power_int(X0),X1) != hAPP_nat_int(power_power_int(X0),X2) ) ),
    inference(cnf_transformation,[],[f3279]) ).

tcf(c_713,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_real(power_power_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3287]) ).

tcf(c_714,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3288]) ).

tcf(c_715,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),X2))) ),
    inference(cnf_transformation,[],[f3289]) ).

tcf(c_716,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X2),X0)),hAPP_nat_real(power_power_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3290]) ).

tcf(c_717,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X2),X0)),hAPP_nat_nat(power_power_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3291]) ).

tcf(c_718,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X2),X0)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3292]) ).

tcf(c_719,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4653]) ).

tcf(c_720,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X2)) ),
    inference(cnf_transformation,[],[f4654]) ).

tcf(c_721,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ( X0 = one_one_int )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
    inference(cnf_transformation,[],[f4655]) ).

tcf(c_722,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),zero_zero_real)) ),
    inference(cnf_transformation,[],[f4656]) ).

tcf(c_723,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),pls)) ),
    inference(cnf_transformation,[],[f4657]) ).

tcf(c_724,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ( sK12(X0) != one_one_int ) ),
    inference(cnf_transformation,[],[f3304]) ).

tcf(c_725,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ( sK12(X0) != X0 ) ),
    inference(cnf_transformation,[],[f3303]) ).

tcf(c_726,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK12(X0)))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4658]) ).

tcf(c_727,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK12(X0)),X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3301]) ).

tcf(c_728,plain,
    ! [X0: $i] :
      ( is_int(sK12(X0))
      | hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3300]) ).

tcf(c_729,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f3299]) ).

tcf(c_730,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4659]) ).

tcf(c_731,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X2)) != X1 ) ),
    inference(cnf_transformation,[],[f4660]) ).

tcf(c_732,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X2)) != X1 ) ),
    inference(cnf_transformation,[],[f4661]) ).

tcf(c_733,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(cnf_transformation,[],[f4662]) ).

tcf(c_734,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK13),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),number_number_of_int(min)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int))),
    inference(cnf_transformation,[],[f4663]) ).

tcf(c_735,plain,
    is_int(sK13),
    inference(cnf_transformation,[],[f3308]) ).

tcf(c_736,plain,
    legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)) = one_one_int,
    inference(cnf_transformation,[],[f4664]) ).

tcf(c_738,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),zero_zero_nat))),
    inference(cnf_transformation,[],[f5018]) ).

tcf(c_741,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3315]) ).

tcf(c_742,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f3314]) ).

tcf(c_743,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X0))))
      | ( number_number_of_nat(X0) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3319]) ).

tcf(c_746,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3320]) ).

tcf(c_747,plain,
    ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),min)),min) = min )
    | ~ is_int(min) ),
    inference(cnf_transformation,[],[f5020]) ).

tcf(c_748,plain,
    ! [X0: $i] :
      ( ( X0 = min )
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) != min ) ),
    inference(cnf_transformation,[],[f4666]) ).

tcf(c_751,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),min)),min) = min,
    inference(cnf_transformation,[],[f4669]) ).

tcf(c_753,plain,
    pls != min,
    inference(cnf_transformation,[],[f3327]) ).

tcf(c_755,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != min,
    inference(cnf_transformation,[],[f4671]) ).

tcf(c_756,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
    inference(cnf_transformation,[],[f3330]) ).

tcf(c_759,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
      | ( X0 = zero_zero_real ) ),
    inference(cnf_transformation,[],[f3332]) ).

tcf(c_760,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(cnf_transformation,[],[f4672]) ).

tcf(c_761,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(cnf_transformation,[],[f4673]) ).

tcf(c_762,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f4674]) ).

tcf(c_763,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(cnf_transformation,[],[f4675]) ).

tcf(c_764,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
    inference(cnf_transformation,[],[f3338]) ).

tcf(c_766,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f4676]) ).

tcf(c_767,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(cnf_transformation,[],[f4677]) ).

tcf(c_768,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
    inference(cnf_transformation,[],[f4678]) ).

tcf(c_769,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f4679]) ).

tcf(c_770,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(cnf_transformation,[],[f4680]) ).

tcf(c_771,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(cnf_transformation,[],[f4681]) ).

tcf(c_772,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(cnf_transformation,[],[f4682]) ).

tcf(c_773,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
    inference(cnf_transformation,[],[f3347]) ).

tcf(c_774,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
    inference(cnf_transformation,[],[f3348]) ).

tcf(c_775,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f4683]) ).

tcf(c_776,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(cnf_transformation,[],[f4684]) ).

tcf(c_777,plain,
    number_number_of_int(pls) != number_number_of_int(min),
    inference(cnf_transformation,[],[f3351]) ).

tcf(c_778,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3352]) ).

tcf(c_780,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) = one_one_nat,
    inference(cnf_transformation,[],[f3354]) ).

tcf(c_782,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),zero_zero_nat) = one_one_real,
    inference(cnf_transformation,[],[f3356]) ).

tcf(c_784,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),zero_zero_nat) = one_one_int,
    inference(cnf_transformation,[],[f3358]) ).

tcf(c_786,plain,
    number_number_of_nat(pls) = zero_zero_nat,
    inference(cnf_transformation,[],[f3360]) ).

tcf(c_787,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(cnf_transformation,[],[f4685]) ).

tcf(c_788,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(cnf_transformation,[],[f4686]) ).

tcf(c_789,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(cnf_transformation,[],[f4687]) ).

tcf(c_790,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(cnf_transformation,[],[f4688]) ).

tcf(c_791,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ( number_number_of_int(min) = X0 )
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f3365]) ).

tcf(c_792,plain,
    ( ( hAPP_int_int(times_times_int(one_one_int),one_one_int) = one_one_int )
    | ~ is_int(one_one_int) ),
    inference(cnf_transformation,[],[f5155]) ).

tcf(c_793,plain,
    ( ( hAPP_int_int(times_times_int(number_number_of_int(min)),number_number_of_int(min)) = one_one_int )
    | ~ is_int(number_number_of_int(min)) ),
    inference(cnf_transformation,[],[f5156]) ).

tcf(c_795,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ( number_number_of_int(min) = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f3368]) ).

tcf(c_796,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_int )
      | ( number_number_of_int(min) = X0 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f3367]) ).

tcf(c_797,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_int )
      | ( number_number_of_int(min) = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f3366]) ).

tcf(c_798,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3372]) ).

tcf(c_799,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0)) ),
    inference(cnf_transformation,[],[f3373]) ).

tcf(c_800,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3374]) ).

tcf(c_801,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_nat_real(power_power_real(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3376]) ).

tcf(c_803,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(power_power_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3378]) ).

tcf(c_805,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(power_power_int(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3380]) ).

tcf(c_807,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f3382]) ).

tcf(c_808,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(cnf_transformation,[],[f3381]) ).

tcf(c_811,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3386]) ).

tcf(c_812,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( number_number_of_nat(X0) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3385]) ).

tcf(c_814,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3387]) ).

tcf(c_815,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
    inference(cnf_transformation,[],[f3389]) ).

tcf(c_817,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(cnf_transformation,[],[f4689]) ).

tcf(c_818,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),X2)) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3393]) ).

tcf(c_819,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),hAPP_nat_nat(times_times_nat(number_number_of_nat(X1)),X2)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(X0),X1))),X2) ) ),
    inference(cnf_transformation,[],[f3392]) ).

tcf(c_820,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3395]) ).

tcf(c_821,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(hAPP_int_int(times_times_int(X0),X1)) ) ),
    inference(cnf_transformation,[],[f3394]) ).

tcf(c_828,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),pls)) ),
    inference(cnf_transformation,[],[f4692]) ).

tcf(c_829,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
    inference(cnf_transformation,[],[f3403]) ).

tcf(c_830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X3),X0),hAPP_int_int(times_times_int(X4),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X3,X4),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3404]) ).

tcf(c_831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X3),X0),hAPP_int_int(times_times_int(X3),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3405]) ).

tcf(c_832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X3),hAPP_int_int(times_times_int(X1),X3)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3406]) ).

tcf(c_833,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),X1)),X1)),
    inference(cnf_transformation,[],[f3407]) ).

tcf(c_834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X3),X0),hAPP_int_int(plus_plus_int(X4),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X3,X4),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3408]) ).

tcf(c_835,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = one_one_real,
    inference(cnf_transformation,[],[f4693]) ).

tcf(c_836,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = one_one_int,
    inference(cnf_transformation,[],[f4694]) ).

tcf(c_839,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_nat(X0) != zero_zero_nat )
      | ( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X0)) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3411]) ).

tcf(c_842,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_nat(X0) != zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X0)) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3414]) ).

tcf(c_845,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_int(X1)
      | ( number_number_of_nat(X0) != zero_zero_nat )
      | ( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X0)) != pls ) ),
    inference(cnf_transformation,[],[f4697]) ).

tcf(c_846,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
    inference(cnf_transformation,[],[f4698]) ).

tcf(c_848,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4700]) ).

tcf(c_849,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4701]) ).

tcf(c_850,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4702]) ).

tcf(c_851,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X2))),X1))
      | ~ is_int(X2)
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(cnf_transformation,[],[f5034]) ).

tcf(c_852,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK14(X0,X1,X2))
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3426]) ).

tcf(c_853,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X2),sK14(X0,X1,X2))) = X1 )
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3425]) ).

tcf(c_854,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real )
      | ( number_number_of_nat(X0) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3429]) ).

tcf(c_855,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real ) ),
    inference(cnf_transformation,[],[f3428]) ).

tcf(c_856,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat )
      | ( number_number_of_nat(X0) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3431]) ).

tcf(c_857,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3430]) ).

tcf(c_858,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = one_one_int )
      | ( number_number_of_nat(X0) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f4703]) ).

tcf(c_859,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = pls ) ),
    inference(cnf_transformation,[],[f4704]) ).

tcf(c_860,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4705]) ).

tcf(c_862,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
    inference(cnf_transformation,[],[f4707]) ).

tcf(c_863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)),pls))
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5) ) ),
    inference(cnf_transformation,[],[f4708]) ).

tcf(c_864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4))) ),
    inference(cnf_transformation,[],[f4709]) ).

tcf(c_865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5) ) ),
    inference(cnf_transformation,[],[f4710]) ).

tcf(c_866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X3)),X4))) ),
    inference(cnf_transformation,[],[f4711]) ).

tcf(c_867,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),pls)) ),
    inference(cnf_transformation,[],[f4712]) ).

tcf(c_868,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2))) ),
    inference(cnf_transformation,[],[f4713]) ).

tcf(c_870,plain,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),number_number_of_int(min))),
    inference(cnf_transformation,[],[f4715]) ).

tcf(c_872,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X2) )
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X1),hAPP_nat_int(power_power_int(number_number_of_int(min)),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4717]) ).

tcf(c_873,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4718]) ).

tcf(c_874,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4719]) ).

tcf(c_875,plain,
    hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),number_number_of_int(min)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int),
    inference(cnf_transformation,[],[f4720]) ).

tcf(c_876,plain,
    ( hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),number_number_of_int(min)))
    | ( legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)) != one_one_int ) ),
    inference(cnf_transformation,[],[f4721]) ).

tcf(c_877,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),X1) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f5035]) ).

tcf(c_878,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(minus_minus_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(minus_minus_int(X0),X1)),
    inference(cnf_transformation,[],[f3452]) ).

tcf(c_879,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),X1)),
    inference(cnf_transformation,[],[f3453]) ).

tcf(c_880,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),pls) = X0 )
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f3454]) ).

tcf(c_882,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)) = hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),X2)),
    inference(cnf_transformation,[],[f3456]) ).

tcf(c_883,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f3457]) ).

tcf(c_884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X3),X0),hAPP_int_int(minus_minus_int(X4),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X3,X4),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3458]) ).

tcf(c_885,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2))) ),
    inference(cnf_transformation,[],[f3459]) ).

tcf(c_886,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(X0)),X1)),hAPP_real_real(times_times_real(number267125858f_real(X0)),X2)) = hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(X1),X2)),
    inference(cnf_transformation,[],[f3460]) ).

tcf(c_888,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X0),number267125858f_real(X1))),hAPP_real_real(times_times_real(X2),number267125858f_real(X1))) = hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X0),X2)),number267125858f_real(X1)),
    inference(cnf_transformation,[],[f3462]) ).

tcf(c_890,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(X0),X1))),hAPP_int_int(minus_minus_int(X0),X1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(cnf_transformation,[],[f4723]) ).

tcf(c_891,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)),
    inference(cnf_transformation,[],[f4724]) ).

tcf(c_892,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(pls),X0)),hAPP_int_int(minus_minus_int(pls),X0)) = hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(cnf_transformation,[],[f4725]) ).

tcf(c_893,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls)) ),
    inference(cnf_transformation,[],[f4726]) ).

tcf(c_894,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4727]) ).

tcf(c_895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3))),hAPP_int_int(times_times_int(X4),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X5),X1)),hAPP_int_int(times_times_int(X6),X3)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X4),X5))),X1)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X2),hAPP_int_int(times_times_int(X4),X6))),X3)),
    inference(cnf_transformation,[],[f3469]) ).

tcf(c_896,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2))) ),
    inference(cnf_transformation,[],[f3471]) ).

tcf(c_897,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3470]) ).

tcf(c_898,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(minus_minus_real(number267125858f_real(X1)),X2)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f3472]) ).

tcf(c_899,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),X2)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),X2),
    inference(cnf_transformation,[],[f3473]) ).

tcf(c_900,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ( hAPP_int_int(minus_minus_int(X1),one_one_int) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4728]) ).

tcf(c_901,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3476]) ).

tcf(c_903,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(min),X0))),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(cnf_transformation,[],[f4729]) ).

tcf(c_904,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(min),X0))),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(cnf_transformation,[],[f4730]) ).

tcf(c_905,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),X0)),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),
    inference(cnf_transformation,[],[f4731]) ).

tcf(c_906,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1)) ),
    inference(cnf_transformation,[],[f3481]) ).

tcf(c_907,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),one_one_int)),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f3480]) ).

tcf(c_908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X3),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X3),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f5036]) ).

tcf(c_909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X3)),hAPP_int_int(times_times_int(X2),X1)))) = hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X2))),twoSqu1241645765sum2sq(product_Pair_int_int(X1,X3))),
    inference(cnf_transformation,[],[f3483]) ).

tcf(c_910,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f4732]) ).

tcf(c_911,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ( hAPP_int_int(minus_minus_int(X1),one_one_int) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1)) ),
    inference(cnf_transformation,[],[f4733]) ).

tcf(c_912,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)),
    inference(cnf_transformation,[],[f4734]) ).

tcf(c_913,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)),
    inference(cnf_transformation,[],[f4735]) ).

tcf(c_914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X4),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X4,X1),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f3489]) ).

tcf(c_915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X4),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X4),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f3488]) ).

tcf(c_916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X4)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X4,X2),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f3491]) ).

tcf(c_917,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X4)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X2,X4),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f3490]) ).

tcf(c_918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X0),X3),hAPP_int_int(plus_plus_int(X1),X3)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3492]) ).

tcf(c_919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),X3),hAPP_nat_int(power_power_int(X1),X3)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f3493]) ).

tcf(c_920,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)) = hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4736]) ).

tcf(c_921,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1)) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4737]) ).

tcf(c_922,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4738]) ).

tcf(c_923,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),X1))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
    inference(cnf_transformation,[],[f4739]) ).

tcf(c_924,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4740]) ).

tcf(c_925,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4741]) ).

tcf(c_926,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4742]) ).

tcf(c_929,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4745]) ).

tcf(c_930,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(cnf_transformation,[],[f4746]) ).

tcf(c_931,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(cnf_transformation,[],[f3505]) ).

tcf(c_932,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4747]) ).

tcf(c_933,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3507]) ).

tcf(c_934,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = one_one_int )
      | ( hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = number_number_of_int(min) ) ),
    inference(cnf_transformation,[],[f3508]) ).

tcf(c_935,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),pls),X2)) ),
    inference(cnf_transformation,[],[f4748]) ).

tcf(c_939,plain,
    ! [X0: $i] :
      ( ( legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int))) ),
    inference(cnf_transformation,[],[f4751]) ).

tcf(c_940,plain,
    ! [X0: $i,X1: $i] :
      ( ( legendre(X0,X1) = pls )
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(cnf_transformation,[],[f4752]) ).

tcf(c_941,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | ( legendre(X1,X0) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(cnf_transformation,[],[f4753]) ).

tcf(c_942,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(quadRes(X1),X0))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ( legendre(X0,X1) = number_number_of_int(min) ) ),
    inference(cnf_transformation,[],[f4754]) ).

tcf(c_943,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)),X1))
      | ( X1 = zero_zero_nat )
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4755]) ).

tcf(c_944,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X2)) ),
    inference(cnf_transformation,[],[f4756]) ).

tcf(c_945,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK15(X0,X1))
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(cnf_transformation,[],[f3519]) ).

tcf(c_946,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X0))
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(cnf_transformation,[],[f4757]) ).

tcf(c_948,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f4759]) ).

tcf(c_949,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f4760]) ).

tcf(c_950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X4)),hAPP_real_real(times_times_real(X1),X2))),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X4),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3))
      | ( hAPP_real_real(plus_plus_real(X0),X1) != one_one_real ) ),
    inference(cnf_transformation,[],[f3524]) ).

tcf(c_951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X4)),hAPP_int_int(times_times_int(X1),X2))),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
      | ( hAPP_int_int(plus_plus_int(X0),X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f4761]) ).

tcf(c_952,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),zero_zero_real)),
    inference(cnf_transformation,[],[f3526]) ).

tcf(c_954,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),pls)),
    inference(cnf_transformation,[],[f4762]) ).

tcf(c_955,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3530]) ).

tcf(c_956,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3529]) ).

tcf(c_957,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f3531]) ).

tcf(c_959,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X0)),
    inference(cnf_transformation,[],[f3533]) ).

tcf(c_961,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X0)),
    inference(cnf_transformation,[],[f3535]) ).

tcf(c_962,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3536]) ).

tcf(c_964,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3538]) ).

tcf(c_969,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3545]) ).

tcf(c_970,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3544]) ).

tcf(c_971,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X0)),
    inference(cnf_transformation,[],[f5040]) ).

tcf(c_975,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)),
    inference(cnf_transformation,[],[f3549]) ).

tcf(c_976,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),X1) = hAPP_real_real(times_times_real(X1),X0),
    inference(cnf_transformation,[],[f3550]) ).

tcf(c_977,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(one_one_real),X0) = X0,
    inference(cnf_transformation,[],[f3551]) ).

tcf(c_978,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X2),X0)),hAPP_real_real(plus_plus_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3552]) ).

tcf(c_979,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_nat(power_power_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3553]) ).

tcf(c_980,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_real(power_power_real(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3554]) ).

tcf(c_981,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_int(power_power_int(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3555]) ).

tcf(c_983,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),one_one_nat)),X0)) = hAPP_nat_nat(times_times_nat(X1),X0) ) ),
    inference(cnf_transformation,[],[f3556]) ).

tcf(c_985,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),one_one_nat))) = hAPP_nat_nat(power_power_nat(X0),X1) ) ),
    inference(cnf_transformation,[],[f3558]) ).

tcf(c_986,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)),
    inference(cnf_transformation,[],[f4763]) ).

tcf(c_995,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),X1) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3567]) ).

tcf(c_998,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4768]) ).

tcf(c_999,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(X0),zero_zero_real) = zero_zero_real,
    inference(cnf_transformation,[],[f3573]) ).

tcf(c_1001,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),pls) = pls,
    inference(cnf_transformation,[],[f4769]) ).

tcf(c_1002,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(zero_zero_real),X0) = zero_zero_real,
    inference(cnf_transformation,[],[f3576]) ).

tcf(c_1004,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(pls),X0) = pls,
    inference(cnf_transformation,[],[f4770]) ).

tcf(c_1008,plain,
    one_one_real != zero_zero_real,
    inference(cnf_transformation,[],[f3582]) ).

tcf(c_1009,plain,
    one_one_nat != zero_zero_nat,
    inference(cnf_transformation,[],[f3583]) ).

tcf(c_1010,plain,
    one_one_int != pls,
    inference(cnf_transformation,[],[f4772]) ).

tcf(c_1011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X2),X1)),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f3585]) ).

tcf(c_1012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f3586]) ).

tcf(c_1013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X1)),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f3587]) ).

tcf(c_1016,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f3590]) ).

tcf(c_1017,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f3591]) ).

tcf(c_1019,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4773]) ).

tcf(c_1020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(X0),X1)),hAPP_real_real(minus_minus_real(X2),X3)) = hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(X0),X2)),hAPP_real_real(plus_plus_real(X1),X3)),
    inference(cnf_transformation,[],[f3594]) ).

tcf(c_1021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_int_int(minus_minus_int(X2),X3)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X2)),hAPP_int_int(plus_plus_int(X1),X3)),
    inference(cnf_transformation,[],[f3595]) ).

tcf(c_1022,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3596]) ).

tcf(c_1023,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3597]) ).

tcf(c_1024,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3598]) ).

tcf(c_1025,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3599]) ).

tcf(c_1026,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3600]) ).

tcf(c_1027,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3601]) ).

tcf(c_1031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3605]) ).

tcf(c_1032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3606]) ).

tcf(c_1033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3607]) ).

tcf(c_1034,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3608]) ).

tcf(c_1035,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3609]) ).

tcf(c_1036,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3610]) ).

tcf(c_1037,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3611]) ).

tcf(c_1038,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3612]) ).

tcf(c_1039,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3613]) ).

tcf(c_1040,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X0))),
    inference(cnf_transformation,[],[f3614]) ).

tcf(c_1041,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X0))),
    inference(cnf_transformation,[],[f3615]) ).

tcf(c_1042,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X0))),
    inference(cnf_transformation,[],[f3616]) ).

tcf(c_1043,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X0),X1))),
    inference(cnf_transformation,[],[f3617]) ).

tcf(c_1044,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X0),X1))),
    inference(cnf_transformation,[],[f3618]) ).

tcf(c_1045,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X0),X1))),
    inference(cnf_transformation,[],[f3619]) ).

tcf(c_1046,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3620]) ).

tcf(c_1047,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3621]) ).

tcf(c_1048,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3622]) ).

tcf(c_1049,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),X0)),
    inference(cnf_transformation,[],[f3623]) ).

tcf(c_1051,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X0)),
    inference(cnf_transformation,[],[f3625]) ).

tcf(c_1052,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(minus_minus_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3626]) ).

tcf(c_1053,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f3627]) ).

tcf(c_1054,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_real )
      | ( X0 = X2 )
      | ( hAPP_real_real(times_times_real(X0),X1) != hAPP_real_real(times_times_real(X2),X1) ) ),
    inference(cnf_transformation,[],[f3628]) ).

tcf(c_1055,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),X1) != hAPP_real_real(times_times_real(X0),X2) ) ),
    inference(cnf_transformation,[],[f3630]) ).

tcf(c_1056,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f3632]) ).

tcf(c_1062,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X2)),X1),
    inference(cnf_transformation,[],[f3638]) ).

tcf(c_1063,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) = zero_zero_nat ) ),
    inference(cnf_transformation,[],[f5056]) ).

tcf(c_1065,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3639]) ).

tcf(c_1066,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3642]) ).

tcf(c_1069,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3646]) ).

tcf(c_1070,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3645]) ).

tcf(c_1071,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4774]) ).

tcf(c_1072,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4775]) ).

tcf(c_1077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3653]) ).

tcf(c_1079,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4778]) ).

tcf(c_1080,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X3),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3656]) ).

tcf(c_1082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X3),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4779]) ).

tcf(c_1083,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X2),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3659]) ).

tcf(c_1084,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4780]) ).

tcf(c_1085,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X2)),hAPP_real_real(times_times_real(X0),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3661]) ).

tcf(c_1086,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4781]) ).

tcf(c_1089,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4782]) ).

tcf(c_1090,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3666]) ).

tcf(c_1093,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3669]) ).

tcf(c_1095,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4784]) ).

tcf(c_1110,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3691]) ).

tcf(c_1111,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3690]) ).

tcf(c_1113,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3688]) ).

tcf(c_1114,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3687]) ).

tcf(c_1119,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),pls)) ),
    inference(cnf_transformation,[],[f4793]) ).

tcf(c_1120,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),pls)) ),
    inference(cnf_transformation,[],[f4794]) ).

tcf(c_1122,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f3703]) ).

tcf(c_1123,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3702]) ).

tcf(c_1125,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f3700]) ).

tcf(c_1126,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f3699]) ).

tcf(c_1128,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4796]) ).

tcf(c_1129,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4797]) ).

tcf(c_1131,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f4799]) ).

tcf(c_1132,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f4800]) ).

tcf(c_1134,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0))),
    inference(cnf_transformation,[],[f3710]) ).

tcf(c_1135,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X0))),
    inference(cnf_transformation,[],[f4802]) ).

tcf(c_1149,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3725]) ).

tcf(c_1150,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4808]) ).

tcf(c_1153,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4809]) ).

tcf(c_1155,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3730]) ).

tcf(c_1157,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4811]) ).

tcf(c_1158,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f3734]) ).

tcf(c_1160,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(cnf_transformation,[],[f4812]) ).

tcf(c_1161,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X1))) ),
    inference(cnf_transformation,[],[f3737]) ).

tcf(c_1164,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3740]) ).

tcf(c_1167,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(cnf_transformation,[],[f3743]) ).

tcf(c_1169,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4815]) ).

tcf(c_1172,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4816]) ).

tcf(c_1174,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3749]) ).

tcf(c_1176,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4818]) ).

tcf(c_1178,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X1)),hAPP_real_real(times_times_real(X2),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3757]) ).

tcf(c_1179,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3756]) ).

tcf(c_1180,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3755]) ).

tcf(c_1181,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3754]) ).

tcf(c_1182,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3753]) ).

tcf(c_1183,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4819]) ).

tcf(c_1184,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4820]) ).

tcf(c_1185,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4821]) ).

tcf(c_1186,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4822]) ).

tcf(c_1187,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4823]) ).

tcf(c_1188,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f3759]) ).

tcf(c_1190,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X1),X2)),hAPP_real_real(times_times_real(X0),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3769]) ).

tcf(c_1191,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3768]) ).

tcf(c_1192,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3767]) ).

tcf(c_1193,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3766]) ).

tcf(c_1194,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3765]) ).

tcf(c_1195,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4824]) ).

tcf(c_1196,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4825]) ).

tcf(c_1197,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f4826]) ).

tcf(c_1198,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f4827]) ).

tcf(c_1199,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f4828]) ).

tcf(c_1200,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X1))) ),
    inference(cnf_transformation,[],[f3771]) ).

tcf(c_1201,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X0)),zero_zero_real)),
    inference(cnf_transformation,[],[f3777]) ).

tcf(c_1202,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X0)),pls)),
    inference(cnf_transformation,[],[f4829]) ).

tcf(c_1204,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4830]) ).

tcf(c_1207,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3783]) ).

tcf(c_1208,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f3782]) ).

tcf(c_1209,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3786]) ).

tcf(c_1210,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3785]) ).

tcf(c_1211,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X2)),hAPP_real_real(times_times_real(X1),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3788]) ).

tcf(c_1212,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X1))) ),
    inference(cnf_transformation,[],[f3787]) ).

tcf(c_1213,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3790]) ).

tcf(c_1214,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),X2))) ),
    inference(cnf_transformation,[],[f3789]) ).

tcf(c_1215,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X1),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(cnf_transformation,[],[f3791]) ).

tcf(c_1216,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X2),X0)),hAPP_real_real(times_times_real(X2),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3792]) ).

tcf(c_1218,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3794]) ).

tcf(c_1219,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) != zero_zero_real ) ),
    inference(cnf_transformation,[],[f3793]) ).

tcf(c_1220,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3796]) ).

tcf(c_1222,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(one_one_nat),X0) = one_one_nat,
    inference(cnf_transformation,[],[f5061]) ).

tcf(c_1223,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) = one_one_nat,
    inference(cnf_transformation,[],[f5062]) ).

tcf(c_1224,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( X0 = one_one_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != one_one_nat ) ),
    inference(cnf_transformation,[],[f3798]) ).

tcf(c_1225,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X0)),X2))) ),
    inference(cnf_transformation,[],[f5063]) ).

tcf(c_1226,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0))),
    inference(cnf_transformation,[],[f4831]) ).

tcf(c_1227,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK16(X1,X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3804]) ).

tcf(c_1228,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_real(power_power_real(sK16(X1,X0)),X0) = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3803]) ).

tcf(c_1229,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK17(X1,X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3807]) ).

tcf(c_1230,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_real(power_power_real(sK17(X1,X0)),X0) = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3806]) ).

tcf(c_1231,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK17(hAPP_nat_real(power_power_real(X0),X1),X1) = X0 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(cnf_transformation,[],[f5064]) ).

tcf(c_1233,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1)) ),
    inference(cnf_transformation,[],[f3808]) ).

tcf(c_1235,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X0)) ),
    inference(cnf_transformation,[],[f3810]) ).

tcf(c_1236,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    inference(cnf_transformation,[],[f3812]) ).

tcf(c_1239,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f3815]) ).

tcf(c_1240,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
    inference(cnf_transformation,[],[f3816]) ).

tcf(c_1241,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3817]) ).

tcf(c_1242,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3818]) ).

tcf(c_1243,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(cnf_transformation,[],[f3819]) ).

tcf(c_1244,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0) = zero_zero_nat,
    inference(cnf_transformation,[],[f3820]) ).

tcf(c_1245,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),zero_zero_nat) = X0,
    inference(cnf_transformation,[],[f3821]) ).

tcf(c_1246,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),X0) = zero_zero_nat,
    inference(cnf_transformation,[],[f3822]) ).

tcf(c_1247,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(minus_minus_nat(X1),X0) != zero_zero_nat )
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3823]) ).

tcf(c_1259,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f3836]) ).

tcf(c_1261,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3840]) ).

tcf(c_1262,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3841]) ).

tcf(c_1269,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3861]) ).

tcf(c_1280,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3889]) ).

tcf(c_1282,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)),
    inference(cnf_transformation,[],[f5085]) ).

tcf(c_1283,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3891]) ).

tcf(c_1284,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(cnf_transformation,[],[f3892]) ).

tcf(c_1285,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2)),
    inference(cnf_transformation,[],[f3893]) ).

tcf(c_1286,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3894]) ).

tcf(c_1287,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X0),X2) ) ),
    inference(cnf_transformation,[],[f3895]) ).

tcf(c_1288,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X2),X1) ) ),
    inference(cnf_transformation,[],[f3897]) ).

tcf(c_1289,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X1) = X0,
    inference(cnf_transformation,[],[f3899]) ).

tcf(c_1290,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0) = X1,
    inference(cnf_transformation,[],[f3900]) ).

tcf(c_1291,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3901]) ).

tcf(c_1292,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
    inference(cnf_transformation,[],[f3902]) ).

tcf(c_1293,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X2),
    inference(cnf_transformation,[],[f3903]) ).

tcf(c_1295,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3905]) ).

tcf(c_1297,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3907]) ).

tcf(c_1299,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f3909]) ).

tcf(c_1300,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3910]) ).

tcf(c_1301,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3911]) ).

tcf(c_1302,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3912]) ).

tcf(c_1304,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),X1) ) ),
    inference(cnf_transformation,[],[f3913]) ).

tcf(c_1305,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0)) = hAPP_nat_nat(minus_minus_nat(X2),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3915]) ).

tcf(c_1307,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f3916]) ).

tcf(c_1308,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(cnf_transformation,[],[f3918]) ).

tcf(c_1309,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),X1) = hAPP_nat_nat(times_times_nat(X1),X0),
    inference(cnf_transformation,[],[f3919]) ).

tcf(c_1310,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f3920]) ).

tcf(c_1311,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X2)),
    inference(cnf_transformation,[],[f3921]) ).

tcf(c_1316,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( X0 = zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3925]) ).

tcf(c_1317,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
    inference(cnf_transformation,[],[f3927]) ).

tcf(c_1318,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3928]) ).

tcf(c_1319,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3930]) ).

tcf(c_1320,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f3929]) ).

tcf(c_1321,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3931]) ).

tcf(c_1323,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3933]) ).

tcf(c_1324,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3932]) ).

tcf(c_1325,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0,
    inference(cnf_transformation,[],[f3935]) ).

tcf(c_1326,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0,
    inference(cnf_transformation,[],[f3936]) ).

tcf(c_1327,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X0),X1)) = zero_zero_nat,
    inference(cnf_transformation,[],[f3937]) ).

tcf(c_1329,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3938]) ).

tcf(c_1330,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    inference(cnf_transformation,[],[f3940]) ).

tcf(c_1332,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3943]) ).

tcf(c_1333,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3942]) ).

tcf(c_1336,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(zero_zero_nat),X0) = zero_zero_nat,
    inference(cnf_transformation,[],[f5095]) ).

tcf(c_1337,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),zero_zero_nat) = zero_zero_nat,
    inference(cnf_transformation,[],[f5096]) ).

tcf(c_1338,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f3946]) ).

tcf(c_1342,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_nat )
      | ( X0 = X2 )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X2),X1) ) ),
    inference(cnf_transformation,[],[f3952]) ).

tcf(c_1343,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f3955]) ).

tcf(c_1344,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)),
    inference(cnf_transformation,[],[f3956]) ).

tcf(c_1345,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3958]) ).

tcf(c_1346,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3957]) ).

tcf(c_1347,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3959]) ).

tcf(c_1348,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3960]) ).

tcf(c_1349,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3961]) ).

tcf(c_1350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3962]) ).

tcf(c_1351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X3))
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X2),X3) ) ),
    inference(cnf_transformation,[],[f3963]) ).

tcf(c_1352,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3964]) ).

tcf(c_1353,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ) ),
    inference(cnf_transformation,[],[f3965]) ).

tcf(c_1354,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3967]) ).

tcf(c_1355,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f3966]) ).

tcf(c_1358,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
    inference(cnf_transformation,[],[f5101]) ).

tcf(c_1363,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3975]) ).

tcf(c_1364,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3977]) ).

tcf(c_1365,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
    inference(cnf_transformation,[],[f5103]) ).

tcf(c_1367,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f3978]) ).

tcf(c_1368,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3980]) ).

tcf(c_1369,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3982]) ).

tcf(c_1370,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))) ),
    inference(cnf_transformation,[],[f3981]) ).

tcf(c_1371,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f3983]) ).

tcf(c_1372,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f3984]) ).

tcf(c_1373,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))),
    inference(cnf_transformation,[],[f3985]) ).

tcf(c_1375,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))),
    inference(cnf_transformation,[],[f5104]) ).

tcf(c_1376,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3987]) ).

tcf(c_1377,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3990]) ).

tcf(c_1378,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f3989]) ).

tcf(c_1379,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3991]) ).

tcf(c_1380,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3992]) ).

tcf(c_1381,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3993]) ).

tcf(c_1382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X3),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3994]) ).

tcf(c_1385,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3998]) ).

tcf(c_1386,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3997]) ).

tcf(c_1387,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X0)),X1) = hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(minus_minus_nat(X1),X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3999]) ).

tcf(c_1388,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f4001]) ).

tcf(c_1389,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4000]) ).

tcf(c_1390,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4002]) ).

tcf(c_1391,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4003]) ).

tcf(c_1393,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4006]) ).

tcf(c_1394,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f4005]) ).

tcf(c_1398,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X1)),X0) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(minus_minus_nat(X1),X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4010]) ).

tcf(c_1400,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4012]) ).

tcf(c_1401,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f4013]) ).

tcf(c_1402,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),
    inference(cnf_transformation,[],[f4014]) ).

tcf(c_1405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X3),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4017]) ).

tcf(c_1408,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)))),
    inference(cnf_transformation,[],[f4020]) ).

tcf(c_1409,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),X0))),
    inference(cnf_transformation,[],[f4021]) ).

tcf(c_1413,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),one_one_nat) = X0,
    inference(cnf_transformation,[],[f4025]) ).

tcf(c_1415,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != one_one_nat ) ),
    inference(cnf_transformation,[],[f4027]) ).

tcf(c_1416,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != one_one_nat ) ),
    inference(cnf_transformation,[],[f4026]) ).

tcf(c_1417,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(one_one_nat),X0) = X0,
    inference(cnf_transformation,[],[f4029]) ).

tcf(c_1418,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4030]) ).

tcf(c_1421,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f4031]) ).

tcf(c_1422,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X0,sK19(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4039]) ).

tcf(c_1423,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ( hAPP_nat_nat(plus_plus_nat(X1),sK19(X0,X2,X1)) = X2 )
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4038]) ).

tcf(c_1424,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,sK19(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4037]) ).

tcf(c_1425,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK19(X1,X2,X0)) = X2 ) ),
    inference(cnf_transformation,[],[f4036]) ).

tcf(c_1428,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK20(X1,X2,X0)) = X2 ) ),
    inference(cnf_transformation,[],[f4045]) ).

tcf(c_1429,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,sK20(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4044]) ).

tcf(c_1430,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ( hAPP_nat_nat(plus_plus_nat(X1),sK20(X0,X2,X1)) = X2 )
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4043]) ).

tcf(c_1431,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X0,sK20(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4042]) ).

tcf(c_1432,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f4041]) ).

tcf(c_1436,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4050]) ).

tcf(c_1437,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f4049]) ).

tcf(c_1438,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f4048]) ).

tcf(c_1440,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4052]) ).

tcf(c_1441,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4051]) ).

tcf(c_1442,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4056]) ).

tcf(c_1443,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f4055]) ).

tcf(c_1444,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) ),
    inference(cnf_transformation,[],[f4054]) ).

tcf(c_1445,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_nat )
      | ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f4057]) ).

tcf(c_1446,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4058]) ).

tcf(c_1448,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4062]) ).

tcf(c_1449,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4061]) ).

tcf(c_1451,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(times_times_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4065]) ).

tcf(c_1452,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f4064]) ).

tcf(c_1453,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f4063]) ).

tcf(c_1454,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK21(X1,X0)),X1))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4068]) ).

tcf(c_1455,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X2,X1))
      | ~ hBOOL(hAPP_nat_bool(X2,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK21(X1,X2))) ),
    inference(cnf_transformation,[],[f4067]) ).

tcf(c_1456,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(plus_plus_nat(sK21(X1,X0)),one_one_nat)))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4066]) ).

tcf(c_1457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X0)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X3)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3)),X4))) ),
    inference(cnf_transformation,[],[f4070]) ).

tcf(c_1458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X3),X0)),X1)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4))) ),
    inference(cnf_transformation,[],[f4069]) ).

tcf(c_1460,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X0),X2) ) ),
    inference(cnf_transformation,[],[f4071]) ).

tcf(c_1461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X1)),X3),
    inference(cnf_transformation,[],[f4074]) ).

tcf(c_1463,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4078]) ).

tcf(c_1466,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X2),X0)),hAPP_nat_nat(times_times_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4080]) ).

tcf(c_1467,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4079]) ).

tcf(c_1469,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4082]) ).

tcf(c_1471,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2))) ),
    inference(cnf_transformation,[],[f4084]) ).

tcf(c_1472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X3)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),X3)),X4)) ),
    inference(cnf_transformation,[],[f4087]) ).

tcf(c_1473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X3)),X1)),X2)),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4))) ),
    inference(cnf_transformation,[],[f4086]) ).

tcf(c_1474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X4)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)),X3)),X4) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4088]) ).

tcf(c_1476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X3)),X1)),X2) = X4 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X0))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4) ) ),
    inference(cnf_transformation,[],[f4089]) ).

tcf(c_1477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X0)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X3)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3)),X4))) ),
    inference(cnf_transformation,[],[f4092]) ).

tcf(c_1478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X3),X0)),X1)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4))) ),
    inference(cnf_transformation,[],[f4091]) ).

tcf(c_1479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X3)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X4)) = hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)),X4)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4093]) ).

tcf(c_1480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f5119]) ).

tcf(c_1481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X3),X0)),X1)),X4) = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X3))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4) ) ),
    inference(cnf_transformation,[],[f4094]) ).

tcf(c_1482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X3)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X4)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),X3)),X4)) ),
    inference(cnf_transformation,[],[f4097]) ).

tcf(c_1483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X0),X3)),X1)),X2)),X4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X1)),X4))) ),
    inference(cnf_transformation,[],[f4096]) ).

tcf(c_1484,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4832]) ).

tcf(c_1485,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4833]) ).

tcf(c_1486,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))) ),
    inference(cnf_transformation,[],[f5120]) ).

tcf(c_1487,plain,
    ! [X0: $i] :
      ( is_int(sK22(X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(cnf_transformation,[],[f4102]) ).

tcf(c_1488,plain,
    ! [X0: $i] :
      ( is_int(sK23(X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(cnf_transformation,[],[f4101]) ).

tcf(c_1489,plain,
    ! [X0: $i] :
      ( ( twoSqu1241645765sum2sq(product_Pair_int_int(sK22(X0),sK23(X0))) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(cnf_transformation,[],[f4100]) ).

tcf(c_1500,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | ( X0 = pls )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(cnf_transformation,[],[f4844]) ).

tcf(c_1501,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X0)),hAPP_int_int(times_times_int(X2),X1)))
      | ( X2 = pls )
      | ~ is_int(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4845]) ).

tcf(c_1503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_int_bool(X0,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK24(X0,X1)),X1))) ),
    inference(cnf_transformation,[],[f4847]) ).

tcf(c_1504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X2,sK24(X2,X1)))
      | hBOOL(hAPP_int_bool(X2,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(X2,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4848]) ).

tcf(c_1505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( is_int(sK24(X2,X1))
      | hBOOL(hAPP_int_bool(X2,hAPP_int_int(minus_minus_int(X3),hAPP_int_int(times_times_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(X2,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4849]) ).

tcf(c_1506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_int_bool(X0,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK25(X0,X1)),X1))) ),
    inference(cnf_transformation,[],[f4850]) ).

tcf(c_1507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X2,sK25(X2,X1)))
      | hBOOL(hAPP_int_bool(X2,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(X2,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4851]) ).

tcf(c_1508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( is_int(sK25(X2,X1))
      | hBOOL(hAPP_int_bool(X2,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(X2,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4852]) ).

tcf(c_1509,plain,
    ! [X0: $i] :
      ( is_int(sK26(X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4129]) ).

tcf(c_1510,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,sK26(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4128]) ).

tcf(c_1511,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4127]) ).

tcf(c_1512,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X1,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4853]) ).

tcf(c_1513,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK27(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4854]) ).

tcf(c_1514,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X1,X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4855]) ).

tcf(c_1515,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,sK27(X1,X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4856]) ).

tcf(c_1516,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sK27(X0,X2) = X1 )
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4857]) ).

tcf(c_1517,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4135]) ).

tcf(c_1518,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f4136]) ).

tcf(c_1519,plain,
    ! [X0: $i] :
      ( ( zfact(X0) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4858]) ).

tcf(c_1520,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_int_int(times_times_int(X0),zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))) = zfact(X0) ) ),
    inference(cnf_transformation,[],[f4859]) ).

tcf(c_1521,plain,
    ! [X0: $i,X1: $i] :
      ( ( inv(X0,inv(X0,X1)) = X1 )
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)) ),
    inference(cnf_transformation,[],[f4860]) ).

tcf(c_1522,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(quadRes(X0),X2))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X2),multInv(X0,X1))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4861]) ).

tcf(c_1523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X0)),X0)),X1),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3)) ),
    inference(cnf_transformation,[],[f4141]) ).

tcf(c_1525,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ( inv(X0,X1) != X1 ) ),
    inference(cnf_transformation,[],[f4143]) ).

tcf(c_1526,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ( inv(X0,X1) != one_one_int ) ),
    inference(cnf_transformation,[],[f4144]) ).

tcf(c_1527,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ( hAPP_int_int(minus_minus_int(X0),one_one_int) != inv(X0,X1) ) ),
    inference(cnf_transformation,[],[f4145]) ).

tcf(c_1528,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4146]) ).

tcf(c_1529,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(X1,X0)),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4147]) ).

tcf(c_1530,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),multInv(X0,X2)),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4862]) ).

tcf(c_1531,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ( inv(X0,X1) != pls ) ),
    inference(cnf_transformation,[],[f4863]) ).

tcf(c_1532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X3),multInv(X0,X1)),hAPP_int_int(times_times_int(X3),multInv(X0,X2))),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4864]) ).

tcf(c_1533,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X2,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),multInv(X0,X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4865]) ).

tcf(c_1534,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(multInv(X0,multInv(X0,X1)),X1),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4866]) ).

tcf(c_1535,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4867]) ).

tcf(c_1536,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4868]) ).

tcf(c_1537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X3),multInv(X0,X1))),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X0,X1)),X1)),X2),hAPP_int_int(times_times_int(multInv(X0,X1)),X3)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4869]) ).

tcf(c_1538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X2,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X2),X3),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X3),multInv(X0,X2))),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4870]) ).

tcf(c_1539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X3,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X3,hAPP_int_int(times_times_int(X2),multInv(X0,X1))),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,hAPP_int_int(times_times_int(X2),multInv(X0,X3))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4871]) ).

tcf(c_1540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X3,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X2,X3),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),multInv(X0,X2)),hAPP_int_int(times_times_int(X1),multInv(X0,X3))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4872]) ).

tcf(c_1541,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X0,X1))),multInv(X0,multInv(X0,X1))),X1),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4873]) ).

tcf(c_1542,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(multInv(X0,multInv(X0,X1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),multInv(X0,X1))),multInv(X0,multInv(X0,X1)))),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4874]) ).

tcf(c_1544,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),multInv(X0,X1)),one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4876]) ).

tcf(c_1545,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(inv(X0,X2),wset(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(member_int(X2,wset(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)) ),
    inference(cnf_transformation,[],[f4877]) ).

tcf(c_1546,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X1,wset(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(member_int(inv(X0,X1),wset(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)) ),
    inference(cnf_transformation,[],[f4878]) ).

tcf(c_1547,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X0,wset(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f4165]) ).

tcf(c_1548,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X0,wset(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X1),one_one_int),X2))) ),
    inference(cnf_transformation,[],[f4166]) ).

tcf(c_1549,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(member_int(X2,wset(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4167]) ).

tcf(c_1550,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(member_int(X2,wset(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4168]) ).

tcf(c_1551,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X0,wset(hAPP_int_int(minus_minus_int(X1),one_one_int),X2)))
      | ( X0 = X1 )
      | ( inv(X2,X1) = X0 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(member_int(X0,wset(X1,X2))) ),
    inference(cnf_transformation,[],[f4169]) ).

tcf(c_1552,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X2,wset(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4170]) ).

tcf(c_1553,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK28(X0,X1)),one_one_int))) ),
    inference(cnf_transformation,[],[f4174]) ).

tcf(c_1554,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X0))
      | hBOOL(hAPP_int_bool(X2,sK28(X2,X1)))
      | ~ hBOOL(hAPP_int_bool(X2,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4173]) ).

tcf(c_1555,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK28(X2,X1)),X1))
      | ~ hBOOL(hAPP_int_bool(X2,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4172]) ).

tcf(c_1556,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X0))
      | is_int(sK28(X2,X1))
      | ~ hBOOL(hAPP_int_bool(X2,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4171]) ).

tcf(c_1557,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK29(X0,X1)),one_one_int))) ),
    inference(cnf_transformation,[],[f4178]) ).

tcf(c_1558,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(X0,sK29(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4177]) ).

tcf(c_1559,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK29(X0,X1)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4176]) ).

tcf(c_1560,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | is_int(sK29(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4175]) ).

tcf(c_1561,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(X0,sK30(X0))) ),
    inference(cnf_transformation,[],[f4181]) ).

tcf(c_1562,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(sK30(X0)),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),sK30(X0))) ),
    inference(cnf_transformation,[],[f4180]) ).

tcf(c_1563,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(X0))
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4179]) ).

tcf(c_1564,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK31(X0,X1)),one_one_int))) ),
    inference(cnf_transformation,[],[f4185]) ).

tcf(c_1565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X1))
      | hBOOL(hAPP_int_bool(X2,sK31(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(X2,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4184]) ).

tcf(c_1566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),sK31(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(X2,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4183]) ).

tcf(c_1567,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X1))
      | is_int(sK31(X2,X0))
      | ~ hBOOL(hAPP_int_bool(X2,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4182]) ).

tcf(c_1568,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(sK32(X0,X1)),one_one_int))) ),
    inference(cnf_transformation,[],[f4189]) ).

tcf(c_1569,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(X0,sK32(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4188]) ).

tcf(c_1570,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sK32(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4187]) ).

tcf(c_1571,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | is_int(sK32(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4186]) ).

tcf(c_1572,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X0,X1)),X2)),hAPP_nat_nat(X0,hAPP_nat_nat(plus_plus_nat(X1),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X0,sK33(X0))),hAPP_nat_nat(X0,sK34(X0)))) ),
    inference(cnf_transformation,[],[f4191]) ).

tcf(c_1573,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK33(X0)),sK34(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X0,X1)),X2)),hAPP_nat_nat(X0,hAPP_nat_nat(plus_plus_nat(X1),X2)))) ),
    inference(cnf_transformation,[],[f4190]) ).

tcf(c_1574,plain,
    ! [X0: $i] :
      ( ( wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0) = d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) )
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(cnf_transformation,[],[f4879]) ).

tcf(c_1575,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK35(X1,X0)),X1))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4195]) ).

tcf(c_1576,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X2,X1))
      | ~ hBOOL(hAPP_nat_bool(X2,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK35(X1,X2))) ),
    inference(cnf_transformation,[],[f4194]) ).

tcf(c_1577,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,sK35(X1,X0)))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4193]) ).

tcf(c_1579,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(member_int(X1,d22set(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4197]) ).

tcf(c_1580,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(member_int(X0,d22set(X1))) ),
    inference(cnf_transformation,[],[f4198]) ).

tcf(c_1581,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X0,d22set(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4199]) ).

tcf(c_1582,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK36(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4201]) ).

tcf(c_1583,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4200]) ).

tcf(c_1590,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4207]) ).

tcf(c_1591,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)),
    inference(cnf_transformation,[],[f4210]) ).

tcf(c_1594,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X0)),
    inference(cnf_transformation,[],[f4213]) ).

tcf(c_1599,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ),
    inference(cnf_transformation,[],[f4219]) ).

tcf(c_1600,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4220]) ).

tcf(c_1602,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X2))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1))) ),
    inference(cnf_transformation,[],[f4221]) ).

tcf(c_1603,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1))) ),
    inference(cnf_transformation,[],[f4223]) ).

tcf(c_1604,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ( X1 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4224]) ).

tcf(c_1605,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != hAPP_nat_nat(times_times_nat(X0),X2) ) ),
    inference(cnf_transformation,[],[f4225]) ).

tcf(c_1606,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0))),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4880]) ).

tcf(c_1607,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)))),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4881]) ).

tcf(c_1608,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) ) ),
    inference(cnf_transformation,[],[f4882]) ).

tcf(c_1609,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X1)),number_number_of_int(X0)))
      | ( hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1)) != pls ) ),
    inference(cnf_transformation,[],[f4883]) ).

tcf(c_1610,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)) = pls )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f4884]) ).

tcf(c_1613,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4887]) ).

tcf(c_1614,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4888]) ).

tcf(c_1615,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),X1)),X0) = pls )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(cnf_transformation,[],[f5125]) ).

tcf(c_1616,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK37(X0,X1))
      | ~ is_int(X0)
      | ( hAPP_int_int(div_mod_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4890]) ).

tcf(c_1617,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),sK37(X0,X1)) = X0 )
      | ~ is_int(X0)
      | ( hAPP_int_int(div_mod_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4891]) ).

tcf(c_1618,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(X1),X0) = hAPP_int_int(div_mod_int(X2),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(X1),X2))) ),
    inference(cnf_transformation,[],[f4240]) ).

tcf(c_1619,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(X0),X2)))
      | ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1) ) ),
    inference(cnf_transformation,[],[f4239]) ).

tcf(c_1620,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X2),X1))
      | ( hAPP_int_int(div_mod_int(X0),X1) != hAPP_int_int(div_mod_int(X2),X1) ) ),
    inference(cnf_transformation,[],[f4241]) ).

tcf(c_1622,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X2),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X1),hAPP_int_int(div_mod_int(X2),X1)),X1)) ),
    inference(cnf_transformation,[],[f4244]) ).

tcf(c_1623,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X2),hAPP_int_int(div_mod_int(X1),X2)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4243]) ).

tcf(c_1624,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(cnf_transformation,[],[f4245]) ).

tcf(c_1625,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(div_mod_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4246]) ).

tcf(c_1626,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f4247]) ).

tcf(c_1628,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),X1)),X2),
    inference(cnf_transformation,[],[f4249]) ).

tcf(c_1629,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(X0),X0) = pls,
    inference(cnf_transformation,[],[f4892]) ).

tcf(c_1630,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(pls),X0) = pls,
    inference(cnf_transformation,[],[f4893]) ).

tcf(c_1631,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(div_mod_int(X1),X2))),X2) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X1)),X2),
    inference(cnf_transformation,[],[f4252]) ).

tcf(c_1632,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(X0),X1)),X2)),X1) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X0),X2)),X1),
    inference(cnf_transformation,[],[f4253]) ).

tcf(c_1633,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(X0),number_number_of_int(min)) = pls,
    inference(cnf_transformation,[],[f4894]) ).

tcf(c_1634,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X2),X1)),X0) = hAPP_int_int(div_mod_int(X2),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4895]) ).

tcf(c_1640,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4901]) ).

tcf(c_1642,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4903]) ).

tcf(c_1643,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4904]) ).

tcf(c_1644,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X1),X0) = X1 )
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4905]) ).

tcf(c_1645,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(div_mod_int(X0),X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(cnf_transformation,[],[f4906]) ).

tcf(c_1646,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1))) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))),
    inference(cnf_transformation,[],[f4907]) ).

tcf(c_1647,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,sK39(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4275]) ).

tcf(c_1648,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK39(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4908]) ).

tcf(c_1649,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK39(X0,X1,X2)),X1)) ),
    inference(cnf_transformation,[],[f4273]) ).

tcf(c_1650,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK38(X1,X0,X2))),sK39(X1,X0,X2)) = X2 ) ),
    inference(cnf_transformation,[],[f4272]) ).

tcf(c_1651,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | is_int(sK38(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f4271]) ).

tcf(c_1652,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | is_int(sK39(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f4270]) ).

tcf(c_1653,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4909]) ).

tcf(c_1654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X0,X3))
      | ~ is_int(X3)
      | ~ is_int(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | ~ sP3(X0,X1,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f5126]) ).

tcf(c_1663,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X2),X1)))
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ sP2(X0,X1,X2)
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4288]) ).

tcf(c_1664,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X2),X1)))
      | ( X1 = pls )
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ sP2(X0,X1,X2)
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4914]) ).

tcf(c_1665,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ is_int(pls)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),pls))) ),
    inference(cnf_transformation,[],[f5128]) ).

tcf(c_1666,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X2,X1)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(cnf_transformation,[],[f4285]) ).

tcf(c_1667,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X2,X1)
      | ~ is_int(X2)
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2))) ),
    inference(cnf_transformation,[],[f4284]) ).

tcf(c_1668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X3),X2))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4916]) ).

tcf(c_1669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X3),X2))),X0)),hAPP_int_int(times_times_int(X1),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4917]) ).

tcf(c_1670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X3),X2))),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4918]) ).

tcf(c_1671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X3),X2))),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4919]) ).

tcf(c_1673,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = pls )
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X0)),X1) = X0 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f5130]) ).

tcf(c_1674,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ( X0 = pls )
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),X1)),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f5131]) ).

tcf(c_1675,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != pls )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != one_one_int ) ),
    inference(cnf_transformation,[],[f4924]) ).

tcf(c_1676,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = pls )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = one_one_int ) ),
    inference(cnf_transformation,[],[f4925]) ).

tcf(c_1677,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) = hAPP_int_int(minus_minus_int(X0),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4926]) ).

tcf(c_1678,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(X1),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4927]) ).

tcf(c_1679,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK42(X0,X1))
      | ~ is_int(X0)
      | ( hAPP_int_int(div_mod_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4928]) ).

tcf(c_1680,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),sK42(X0,X1)) = X0 )
      | ~ is_int(X0)
      | ( hAPP_int_int(div_mod_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4929]) ).

tcf(c_1681,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X1),X0)),hAPP_int_int(div_mod_int(X2),X0)),hAPP_int_int(times_times_int(X1),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(cnf_transformation,[],[f4930]) ).

tcf(c_1682,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X1),X0)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4304]) ).

tcf(c_1683,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X1),X0)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4305]) ).

tcf(c_1684,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X0) = zero_zero_nat,
    inference(cnf_transformation,[],[f5133]) ).

tcf(c_1685,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),sK43(X0,X1)) = X0 )
      | ( hAPP_nat_nat(div_mod_nat(X0),X1) != zero_zero_nat ) ),
    inference(cnf_transformation,[],[f4306]) ).

tcf(c_1688,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X1) = hAPP_nat_nat(div_mod_nat(X0),X1) ) ),
    inference(cnf_transformation,[],[f4309]) ).

tcf(c_1689,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),X1) = hAPP_nat_nat(div_mod_nat(X2),X1),
    inference(cnf_transformation,[],[f4311]) ).

tcf(c_1690,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X0) = hAPP_nat_nat(div_mod_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4312]) ).

tcf(c_1691,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(X0),X2)),X1),
    inference(cnf_transformation,[],[f4314]) ).

tcf(c_1692,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X2)) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(div_mod_nat(X1),X2)),
    inference(cnf_transformation,[],[f4315]) ).

tcf(c_1693,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),X1) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4316]) ).

tcf(c_1694,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X0)),
    inference(cnf_transformation,[],[f4317]) ).

tcf(c_1697,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) = pls )
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(cnf_transformation,[],[f4933]) ).

tcf(c_1698,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ( hAPP_int_int(div_mod_int(X0),X1) != pls ) ),
    inference(cnf_transformation,[],[f4934]) ).

tcf(c_1699,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(div_mod_int(X0),X1)),X1)),
    inference(cnf_transformation,[],[f4935]) ).

tcf(c_1700,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(X1),X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4936]) ).

tcf(c_1701,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(member_int(X0,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),cOMBC_int_int_bool(ord_less_int,X1))))) ),
    inference(cnf_transformation,[],[f4937]) ).

tcf(c_1711,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(div_mod_nat(X0),X2)))
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4336]) ).

tcf(c_1712,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2))) ),
    inference(cnf_transformation,[],[f4335]) ).

tcf(c_1713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(div_mod_nat(X3),X2))),X0)),hAPP_nat_nat(times_times_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4337]) ).

tcf(c_1714,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(cnf_transformation,[],[f4938]) ).

tcf(c_1715,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X2) = hAPP_int_int(div_mod_int(X1),X2) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f4939]) ).

tcf(c_1717,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
      | ~ hBOOL(X1)
      | ~ hBOOL(X0) ),
    inference(cnf_transformation,[],[f4341]) ).

tcf(c_1718,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f4342]) ).

tcf(c_1719,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(X1)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f4343]) ).

tcf(c_1720,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_bool(hAPP_i1948725293t_bool(X0,X1),X2) = hAPP_int_bool(cOMBC_int_int_bool(X0,X2),X1),
    inference(cnf_transformation,[],[f4344]) ).

tcf(c_1721,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_bool_bool(hAPP_i68813070l_bool(X0,X1),hAPP_int_bool(X2,X1)) = hAPP_int_bool(cOMBS_int_bool_bool(X0,X2),X1),
    inference(cnf_transformation,[],[f4345]) ).

tcf(c_1722,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) = hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2),
    inference(cnf_transformation,[],[f4346]) ).

tcf(c_1723,negated_conjecture,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int),
    inference(cnf_transformation,[],[f4941]) ).

tcf(c_2482,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),min)),min) = min,
    inference(global_subsumption_just,[status(thm)],[c_747,c_751]) ).

tcf(c_2495,plain,
    hAPP_int_int(times_times_int(one_one_int),one_one_int) = one_one_int,
    inference(global_subsumption_just,[status(thm)],[c_613,c_49,c_792]) ).

tcf(c_2497,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),pls)))
      | ~ is_int(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_1665,c_57,c_1665]) ).

tcf(c_2498,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),pls))) ),
    inference(renaming,[status(thm)],[c_2497]) ).

tcf(c_2507,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_593,c_594,c_593]) ).

tcf(c_2568,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_1307,c_1295,c_1297,c_1307]) ).

tcf(c_2572,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK17(hAPP_nat_real(power_power_real(X0),X1),X1) = X0 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_1231,c_533,c_1231]) ).

tcf(c_2573,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK17(hAPP_nat_real(power_power_real(X1),X0),X0) = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(renaming,[status(thm)],[c_2572]) ).

tcf(c_2575,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_498,c_1330,c_498]) ).

tcf(c_2583,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1) ) ),
    inference(global_subsumption_just,[status(thm)],[c_480,c_1330,c_480]) ).

tcf(c_2595,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ) ),
    inference(global_subsumption_just,[status(thm)],[c_648,c_1330,c_648]) ).

tcf(c_2597,plain,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),number_number_of_int(min))),
    inference(global_subsumption_just,[status(thm)],[c_876,c_870]) ).

tcf(c_2609,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_131]) ).

tcf(c_2610,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(renaming,[status(thm)],[c_2609]) ).

tcf(c_2615,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_141,c_134]) ).

tcf(c_2616,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_2615]) ).

tcf(c_2617,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_142,c_133]) ).

tcf(c_2618,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_2617]) ).

tcf(c_2623,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_138]) ).

tcf(c_2624,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_2623]) ).

tcf(c_2625,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_137]) ).

tcf(c_2627,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_154]) ).

tcf(c_2628,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(renaming,[status(thm)],[c_2627]) ).

tcf(c_2629,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_153]) ).

tcf(c_2631,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_158]) ).

tcf(c_2632,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(renaming,[status(thm)],[c_2631]) ).

tcf(c_2633,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_157]) ).

tcf(c_2643,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_181]) ).

tcf(c_2644,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2643]) ).

tcf(c_2645,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_180]) ).

tcf(c_2647,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_183]) ).

tcf(c_2648,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(renaming,[status(thm)],[c_2647]) ).

tcf(c_2649,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_182]) ).

tcf(c_2651,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_187]) ).

tcf(c_2652,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_2651]) ).

tcf(c_2653,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_186]) ).

tcf(c_2655,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_191]) ).

tcf(c_2656,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(renaming,[status(thm)],[c_2655]) ).

tcf(c_2657,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_190]) ).

tcf(c_2667,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_617]) ).

tcf(c_2668,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2667]) ).

tcf(c_2669,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_616]) ).

tcf(c_2671,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_263]) ).

tcf(c_2672,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_2671]) ).

tcf(c_2673,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_262]) ).

tcf(c_2675,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_573]) ).

tcf(c_2676,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2675]) ).

tcf(c_2677,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_572]) ).

tcf(c_2679,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_611,c_267]) ).

tcf(c_2680,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_2679]) ).

tcf(c_2681,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_266]) ).

tcf(c_2683,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_611]) ).

tcf(c_2684,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(renaming,[status(thm)],[c_2683]) ).

tcf(c_2685,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612]) ).

tcf(c_2687,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_269]) ).

tcf(c_2688,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(renaming,[status(thm)],[c_2687]) ).

tcf(c_2689,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_268]) ).

tcf(c_2691,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_273]) ).

tcf(c_2692,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))) ),
    inference(renaming,[status(thm)],[c_2691]) ).

tcf(c_2693,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_272]) ).

tcf(c_2695,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_275]) ).

tcf(c_2696,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2695]) ).

tcf(c_2697,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_274]) ).

tcf(c_2703,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_286,c_285]) ).

tcf(c_2704,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ),
    inference(renaming,[status(thm)],[c_2703]) ).

tcf(c_2705,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_287,c_284]) ).

tcf(c_2707,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_286]) ).

tcf(c_2708,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(renaming,[status(thm)],[c_2707]) ).

tcf(c_2709,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_287]) ).

tcf(c_2711,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_290,c_289]) ).

tcf(c_2712,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_2711]) ).

tcf(c_2713,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_291,c_288]) ).

tcf(c_2715,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_290]) ).

tcf(c_2716,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(renaming,[status(thm)],[c_2715]) ).

tcf(c_2717,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_291]) ).

tcf(c_2719,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_294,c_293]) ).

tcf(c_2720,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int)) ),
    inference(renaming,[status(thm)],[c_2719]) ).

tcf(c_2721,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),one_one_int))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_295,c_292]) ).

tcf(c_2723,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_294]) ).

tcf(c_2724,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) ),
    inference(renaming,[status(thm)],[c_2723]) ).

tcf(c_2725,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(prop_impl_just,[status(thm)],[c_295]) ).

tcf(c_2727,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_298,c_297]) ).

tcf(c_2728,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_2727]) ).

tcf(c_2729,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_299,c_296]) ).

tcf(c_2731,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_298]) ).

tcf(c_2732,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0)) ),
    inference(renaming,[status(thm)],[c_2731]) ).

tcf(c_2733,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_299]) ).

tcf(c_2743,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_611,c_619]) ).

tcf(c_2744,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_2743]) ).

tcf(c_2745,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_618]) ).

tcf(c_2747,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_611,c_621]) ).

tcf(c_2748,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(renaming,[status(thm)],[c_2747]) ).

tcf(c_2749,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_620]) ).

tcf(c_2751,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_623]) ).

tcf(c_2752,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2751]) ).

tcf(c_2753,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_622]) ).

tcf(c_2771,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_633]) ).

tcf(c_2772,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
    inference(renaming,[status(thm)],[c_2771]) ).

tcf(c_2773,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_632]) ).

tcf(c_2777,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811]) ).

tcf(c_2779,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_761]) ).

tcf(c_2780,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(renaming,[status(thm)],[c_2779]) ).

tcf(c_2781,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_760]) ).

tcf(c_2783,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_763]) ).

tcf(c_2784,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(renaming,[status(thm)],[c_2783]) ).

tcf(c_2785,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_762]) ).

tcf(c_2791,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_770]) ).

tcf(c_2792,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min)) ),
    inference(renaming,[status(thm)],[c_2791]) ).

tcf(c_2793,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_769]) ).

tcf(c_2795,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_772]) ).

tcf(c_2796,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))) ),
    inference(renaming,[status(thm)],[c_2795]) ).

tcf(c_2797,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_771]) ).

tcf(c_2799,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_776]) ).

tcf(c_2800,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(renaming,[status(thm)],[c_2799]) ).

tcf(c_2801,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_775]) ).

tcf(c_2807,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_790]) ).

tcf(c_2808,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(renaming,[status(thm)],[c_2807]) ).

tcf(c_2809,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_789]) ).

tcf(c_2811,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_611,c_808]) ).

tcf(c_2812,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(renaming,[status(thm)],[c_2811]) ).

tcf(c_2813,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_807]) ).

tcf(c_2815,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_893]) ).

tcf(c_2816,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls)) ),
    inference(renaming,[status(thm)],[c_2815]) ).

tcf(c_2817,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_894]) ).

tcf(c_2833,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1332]) ).

tcf(c_2841,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) = pls )
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1697]) ).

tcf(c_2843,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != one_one_int )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != pls ) ),
    inference(prop_impl_just,[status(thm)],[c_1675]) ).

tcf(c_2844,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != pls )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != one_one_int ) ),
    inference(renaming,[status(thm)],[c_2843]) ).

tcf(c_2845,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = one_one_int )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = pls ) ),
    inference(prop_impl_just,[status(thm)],[c_1676]) ).

tcf(c_2846,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = pls )
      | ( hAPP_int_int(div_mod_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = one_one_int ) ),
    inference(renaming,[status(thm)],[c_2845]) ).

tcf(c_2857,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(X1,X0))
      | ~ is_int(X0) ),
    inference(prop_impl_just,[status(thm)],[c_65]) ).

tcf(c_2889,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),X1) = X0 )
      | ~ is_int(X0) ),
    inference(prop_impl_just,[status(thm)],[c_877]) ).

tcf(c_2899,plain,
    ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) )
    | ( one_one_int != t ) ),
    inference(prop_impl_just,[status(thm)],[c_77]) ).

tcf(c_2905,plain,
    ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int) )
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(prop_impl_just,[status(thm)],[c_80]) ).

tcf(c_2907,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_604,c_132]) ).

tcf(c_2908,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(renaming,[status(thm)],[c_2907]) ).

tcf(c_2927,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_603,c_132]) ).

tcf(c_2928,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(renaming,[status(thm)],[c_2927]) ).

tcf(c_2937,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X1),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_1642]) ).

tcf(c_2949,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_628,c_1484]) ).

tcf(c_2951,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_628,c_1485]) ).

tcf(c_2953,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)))),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_628,c_1607]) ).

tcf(c_2955,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(X0),X1)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1614]) ).

tcf(c_2957,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(X1),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1678]) ).

tcf(c_2975,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_743]) ).

tcf(c_2977,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X0)) != zero_zero_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_839]) ).

tcf(c_2978,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1)) != zero_zero_real ) ),
    inference(renaming,[status(thm)],[c_2977]) ).

tcf(c_2979,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X0)) != zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_842]) ).

tcf(c_2980,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)) != zero_zero_nat ) ),
    inference(renaming,[status(thm)],[c_2979]) ).

tcf(c_2981,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_854]) ).

tcf(c_2983,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_856]) ).

tcf(c_2985,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_811,c_858]) ).

tcf(c_2989,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0))),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_1606]) ).

tcf(c_2991,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_812,c_855]) ).

tcf(c_2992,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real ) ),
    inference(renaming,[status(thm)],[c_2991]) ).

tcf(c_2993,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_812,c_857]) ).

tcf(c_2994,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat ) ),
    inference(renaming,[status(thm)],[c_2993]) ).

tcf(c_2995,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = pls )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_812,c_859]) ).

tcf(c_2996,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = pls ) ),
    inference(renaming,[status(thm)],[c_2995]) ).

tcf(c_3001,plain,
    ! [X0: $i] :
      ( ( wset(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0) = d22set(hAPP_int_int(minus_minus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) )
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1574]) ).

tcf(c_3011,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1511]) ).

tcf(c_3067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(X1),X0)),X2)),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1480]) ).

tcf(c_3141,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_nat(power_power_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_979]) ).

tcf(c_3143,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_real(power_power_real(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_980]) ).

tcf(c_3145,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))),X1) = hAPP_nat_int(power_power_int(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_981]) ).

tcf(c_3223,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_531]) ).

tcf(c_3227,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X1,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1512,c_612]) ).

tcf(c_3229,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK27(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1513]) ).

tcf(c_3231,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X1,X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1514]) ).

tcf(c_3233,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,sK27(X1,X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1515]) ).

tcf(c_3235,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(X1),X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1700]) ).

tcf(c_3237,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1714]) ).

tcf(c_3239,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) = hAPP_int_int(minus_minus_int(X0),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_612,c_1677]) ).

tcf(c_3241,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1653,c_611]) ).

tcf(c_3245,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_948]) ).

tcf(c_3247,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_949]) ).

tcf(c_3249,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)) ),
    inference(prop_impl_just,[status(thm)],[c_683]) ).

tcf(c_3251,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),zero_zero_real)) ),
    inference(prop_impl_just,[status(thm)],[c_684]) ).

tcf(c_3257,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1))),zero_zero_real)) ),
    inference(prop_impl_just,[status(thm)],[c_722]) ).

tcf(c_3263,plain,
    ( ( hAPP_int_int(times_times_int(number_number_of_int(min)),number_number_of_int(min)) = one_one_int )
    | ~ is_int(number_number_of_int(min)) ),
    inference(prop_impl_just,[status(thm)],[c_793]) ).

tcf(c_3297,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_874]) ).

tcf(c_3299,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X1),X0)),hAPP_int_int(div_mod_int(X2),X0)),hAPP_int_int(times_times_int(X1),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_1681]) ).

tcf(c_3311,plain,
    ! [X0: $i] :
      ( ( legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),X0)),one_one_int))) ),
    inference(prop_impl_just,[status(thm)],[c_939]) ).

tcf(c_3315,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),X1),X0))
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_946]) ).

tcf(c_3435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(X3,X0)),X0)),X1),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3)) ),
    inference(prop_impl_just,[status(thm)],[c_1523]) ).

tcf(c_3455,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_1608]) ).

tcf(c_3456,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int)),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) ) ),
    inference(renaming,[status(thm)],[c_3455]) ).

tcf(c_3479,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK39(X0,X1,X2)),X1))
      | sP3(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_1649]) ).

tcf(c_3480,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK39(X0,X1,X2)),X1)) ),
    inference(renaming,[status(thm)],[c_3479]) ).

tcf(c_3555,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK38(X1,X0,X2))),sK39(X1,X0,X2)) = X2 )
      | sP3(X1,X0,X2) ),
    inference(prop_impl_just,[status(thm)],[c_1650]) ).

tcf(c_3556,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK38(X1,X0,X2))),sK39(X1,X0,X2)) = X2 ) ),
    inference(renaming,[status(thm)],[c_3555]) ).

tcf(c_3613,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_652]) ).

tcf(c_3619,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_690]) ).

tcf(c_3621,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_691]) ).

tcf(c_5551,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_2616,c_2625]) ).

tcf(c_5552,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_2618,c_2624]) ).

tcf(c_5571,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_482,c_2685]) ).

tcf(c_5572,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(bin_hyper_res,[status(thm)],[c_576,c_2685]) ).

tcf(c_5574,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(bin_hyper_res,[status(thm)],[c_605,c_2610]) ).

tcf(c_5575,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(bin_hyper_res,[status(thm)],[c_614,c_2685]) ).

tcf(c_5576,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_int )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ( hAPP_int_int(times_times_int(X0),X1) != one_one_int ) ),
    inference(bin_hyper_res,[status(thm)],[c_615,c_2685]) ).

tcf(c_5577,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(X1)) != pls ) ),
    inference(bin_hyper_res,[status(thm)],[c_845,c_2777]) ).

tcf(c_5578,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(bin_hyper_res,[status(thm)],[c_849,c_2685]) ).

tcf(c_5579,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2)),pls)) ),
    inference(bin_hyper_res,[status(thm)],[c_867,c_2685]) ).

tcf(c_5580,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2))) ),
    inference(bin_hyper_res,[status(thm)],[c_868,c_2685]) ).

tcf(c_5581,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ( hAPP_int_int(minus_minus_int(X1),one_one_int) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_900,c_2685]) ).

tcf(c_5582,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,one_one_int),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(minus_minus_int(X1),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_910,c_2685]) ).

tcf(c_5583,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_int )
      | ( hAPP_int_int(minus_minus_int(X1),one_one_int) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X0),one_one_int),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_911,c_2685]) ).

tcf(c_5584,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(bin_hyper_res,[status(thm)],[c_924,c_2685]) ).

tcf(c_5585,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_925,c_2685]) ).

tcf(c_5586,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(bin_hyper_res,[status(thm)],[c_1160,c_2684]) ).

tcf(c_5587,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_1172,c_2685]) ).

tcf(c_5588,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(bin_hyper_res,[status(thm)],[c_1176,c_2685]) ).

tcf(c_5589,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(bin_hyper_res,[status(thm)],[c_1185,c_2684]) ).

tcf(c_5590,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2))) ),
    inference(bin_hyper_res,[status(thm)],[c_1186,c_2684]) ).

tcf(c_5591,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != zero_zero_nat ) ),
    inference(bin_hyper_res,[status(thm)],[c_1247,c_2833]) ).

tcf(c_5592,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),inv(X1,X0)),one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1536,c_2685]) ).

tcf(c_5593,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK37(X0,X1))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1616,c_2841]) ).

tcf(c_5594,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),sK37(X0,X1)) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1617,c_2841]) ).

tcf(c_5595,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(X2),X1)),X0) = hAPP_int_int(div_mod_int(X2),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1634,c_2685]) ).

tcf(c_5596,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(div_mod_int(X0),X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(bin_hyper_res,[status(thm)],[c_1645,c_2685]) ).

tcf(c_5597,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ( X0 = pls )
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X2)),X1)),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1674,c_2684]) ).

tcf(c_5598,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK42(X0,X1))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1679,c_2841]) ).

tcf(c_5599,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),sK42(X0,X1)) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1680,c_2841]) ).

tcf(c_5674,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1486,c_61]) ).

tcf(c_5740,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1070,c_1236]) ).

tcf(c_5741,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1069,c_1236]) ).

tcf(c_5742,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X2),X1)),hAPP_nat_nat(power_power_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_543,c_1236]) ).

tcf(c_5743,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hAPP_nat_nat(power_power_nat(X0),X1) != hAPP_nat_nat(power_power_nat(X2),X1) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_2583,c_1236]) ).

tcf(c_5744,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_540,c_1236]) ).

tcf(c_5746,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_645,c_1236]) ).

tcf(c_5747,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) != hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_2595,c_1236]) ).

tcf(c_6323,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
    inference(backward_subsumption_resolution,[status(thm)],[c_2905,c_1723]) ).

tcf(c_6324,plain,
    one_one_int != t,
    inference(backward_subsumption_resolution,[status(thm)],[c_2899,c_1723]) ).

tcf(c_6365,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),X0)),X1) = pls )
      | ~ is_int(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1615,c_2857]) ).

tcf(c_11078,plain,
    number_number_of_int(min) != pls,
    inference(light_normalisation,[status(thm)],[c_777,c_562]) ).

tcf(c_11147,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
    inference(light_normalisation,[status(thm)],[c_738,c_780]) ).

tcf(c_11223,plain,
    hAPP_int_int(plus_plus_int(min),hAPP_int_int(plus_plus_int(one_one_int),min)) = min,
    inference(demodulation,[status(thm)],[c_2482,c_241]) ).

tcf(c_11295,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = one_one_real,
    inference(demodulation,[status(thm)],[c_400,c_241]) ).

tcf(c_11296,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = one_one_int,
    inference(demodulation,[status(thm)],[c_398,c_241]) ).

tcf(c_11299,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),X0)) != pls,
    inference(demodulation,[status(thm)],[c_332,c_241]) ).

tcf(c_11300,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = one_one_nat,
    inference(demodulation,[status(thm)],[c_178,c_241]) ).

tcf(c_11305,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_1202,c_1720]) ).

tcf(c_11429,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),sK39(X1,X0,X2))) ),
    inference(demodulation,[status(thm)],[c_3480,c_1720]) ).

tcf(c_11468,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(X0),X1)) = X0 )
      | ~ is_int(X0) ),
    inference(demodulation,[status(thm)],[c_2889,c_241]) ).

tcf(c_11495,plain,
    ( ( number_number_of_int(hAPP_int_int(times_times_int(min),min)) = one_one_int )
    | ~ is_int(number_number_of_int(min)) ),
    inference(demodulation,[status(thm)],[c_3263,c_348]) ).

tcf(c_11564,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),sK26(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(demodulation,[status(thm)],[c_3011,c_1720]) ).

tcf(c_11591,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(demodulation,[status(thm)],[c_2772,c_1720]) ).

tcf(c_11598,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2773,c_1720]) ).

tcf(c_11637,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(demodulation,[status(thm)],[c_2752,c_1720]) ).

tcf(c_11644,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2753,c_1720]) ).

tcf(c_11651,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),X0)) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(demodulation,[status(thm)],[c_334,c_241]) ).

tcf(c_11656,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),sK27(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(demodulation,[status(thm)],[c_3231,c_1720]) ).

tcf(c_11687,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(demodulation,[status(thm)],[c_2721,c_1720]) ).

tcf(c_11694,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(demodulation,[status(thm)],[c_2720,c_1720]) ).

tcf(c_11709,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(demodulation,[status(thm)],[c_2705,c_1720]) ).

tcf(c_11716,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(demodulation,[status(thm)],[c_2704,c_1720]) ).

tcf(c_11820,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(demodulation,[status(thm)],[c_3235,c_1720]) ).

tcf(c_11870,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2937,c_1720]) ).

tcf(c_11877,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X0),hAPP_int_int(div_mod_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2955,c_1720]) ).

tcf(c_11972,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)),
    inference(light_normalisation,[status(thm)],[c_1239,c_1291]) ).

tcf(c_12071,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2817,c_1720]) ).

tcf(c_12078,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),X1))) ),
    inference(demodulation,[status(thm)],[c_2816,c_1720]) ).

tcf(c_12101,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(demodulation,[status(thm)],[c_2808,c_1720]) ).

tcf(c_12108,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(demodulation,[status(thm)],[c_2809,c_1720]) ).

tcf(c_12123,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(demodulation,[status(thm)],[c_2800,c_1720]) ).

tcf(c_12130,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(demodulation,[status(thm)],[c_2801,c_1720]) ).

tcf(c_12161,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(pls),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_606,c_241]) ).

tcf(c_12163,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(demodulation,[status(thm)],[c_595,c_1720]) ).

tcf(c_12199,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(demodulation,[status(thm)],[c_2696,c_1720]) ).

tcf(c_12206,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2697,c_1720]) ).

tcf(c_12213,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(demodulation,[status(thm)],[c_2676,c_1720]) ).

tcf(c_12220,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2677,c_1720]) ).

tcf(c_12227,plain,
    hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(min),min)) = min,
    inference(demodulation,[status(thm)],[c_11223,c_238]) ).

tcf(c_12228,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_12161,c_238]) ).

tcf(c_12229,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_12228,c_351]) ).

tcf(c_12449,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(plus_plus_nat(one_one_nat),sK21(X1,X0))))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_1456,c_242]) ).

tcf(c_12497,plain,
    ! [X0: $i] :
      ( ( X0 = min )
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)) != min ) ),
    inference(demodulation,[status(thm)],[c_748,c_232]) ).

tcf(c_12527,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(demodulation,[status(thm)],[c_109,c_232,c_238,c_241,c_243]) ).

tcf(c_12528,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)),
    inference(demodulation,[status(thm)],[c_108,c_232,c_238,c_241]) ).

tcf(c_12529,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),X0)))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(demodulation,[status(thm)],[c_107,c_232,c_238]) ).

tcf(c_12530,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),X0)))) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)),
    inference(demodulation,[status(thm)],[c_106,c_232,c_238]) ).

tcf(c_12733,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2796,c_232]) ).

tcf(c_12740,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(demodulation,[status(thm)],[c_2797,c_232]) ).

tcf(c_12747,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2792,c_232,c_1720]) ).

tcf(c_12754,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(demodulation,[status(thm)],[c_2793,c_232,c_1720]) ).

tcf(c_12761,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2784,c_232]) ).

tcf(c_12768,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(demodulation,[status(thm)],[c_2785,c_232]) ).

tcf(c_12775,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2780,c_232,c_1720]) ).

tcf(c_12782,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(demodulation,[status(thm)],[c_2781,c_232,c_1720]) ).

tcf(c_12841,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))) = number267125858f_real(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_393,c_232,c_234,c_387]) ).

tcf(c_12842,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_392,c_232,c_351]) ).

tcf(c_12843,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2688,c_232]) ).

tcf(c_12850,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2689,c_232]) ).

tcf(c_12857,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2668,c_232,c_1720]) ).

tcf(c_12864,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2669,c_232,c_1720]) ).

tcf(c_12871,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2648,c_232]) ).

tcf(c_12878,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2649,c_232]) ).

tcf(c_12885,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(demodulation,[status(thm)],[c_2644,c_232,c_1720]) ).

tcf(c_12892,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2645,c_232,c_1720]) ).

tcf(c_12945,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2951,c_232,c_12842]) ).

tcf(c_12963,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK39(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK38(X0,X1,X2))) = X2 ) ),
    inference(demodulation,[status(thm)],[c_3556,c_241]) ).

tcf(c_13118,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(demodulation,[status(thm)],[c_2733,c_232,c_238,c_241]) ).

tcf(c_13125,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) ),
    inference(demodulation,[status(thm)],[c_2732,c_232,c_238,c_241]) ).

tcf(c_13132,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(demodulation,[status(thm)],[c_2725,c_232,c_238,c_241]) ).

tcf(c_13139,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(demodulation,[status(thm)],[c_2724,c_232,c_238,c_241]) ).

tcf(c_13146,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(demodulation,[status(thm)],[c_2717,c_232,c_238,c_241]) ).

tcf(c_13153,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) ),
    inference(demodulation,[status(thm)],[c_2716,c_232,c_238,c_241]) ).

tcf(c_13160,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(demodulation,[status(thm)],[c_2709,c_232,c_238,c_241]) ).

tcf(c_13167,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(demodulation,[status(thm)],[c_2708,c_232,c_238,c_241]) ).

tcf(c_13174,plain,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
    inference(demodulation,[status(thm)],[c_197,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_13223,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,X0))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),sK12(X0)))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(demodulation,[status(thm)],[c_727,c_1720]) ).

tcf(c_13340,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(demodulation,[status(thm)],[c_1120,c_1720]) ).

tcf(c_13350,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(demodulation,[status(thm)],[c_1119,c_1720]) ).

tcf(c_13390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),X0)),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_905,c_232]) ).

tcf(c_13391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_904,c_232,c_13390]) ).

tcf(c_13392,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),
    inference(demodulation,[status(thm)],[c_817,c_232,c_238,c_241]) ).

tcf(c_13393,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
    inference(demodulation,[status(thm)],[c_733,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_13434,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_2692,c_232]) ).

tcf(c_13441,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2693,c_232]) ).

tcf(c_13448,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(demodulation,[status(thm)],[c_2672,c_232]) ).

tcf(c_13455,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2673,c_232]) ).

tcf(c_13468,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_2656,c_232]) ).

tcf(c_13475,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2657,c_232]) ).

tcf(c_13482,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(demodulation,[status(thm)],[c_2652,c_232]) ).

tcf(c_13489,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2653,c_232]) ).

tcf(c_13676,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_1169,c_1720]) ).

tcf(c_13704,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_1153,c_1720]) ).

tcf(c_13756,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_1072,c_1720]) ).

tcf(c_13766,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_1071,c_1720]) ).

tcf(c_13824,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_int(power_power_int(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(demodulation,[status(thm)],[c_3145,c_220]) ).

tcf(c_13831,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_real(power_power_real(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(demodulation,[status(thm)],[c_3143,c_222]) ).

tcf(c_13838,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_nat(power_power_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(demodulation,[status(thm)],[c_3141,c_221]) ).

tcf(c_13926,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
    inference(demodulation,[status(thm)],[c_150,c_232,c_238,c_241]) ).

tcf(c_13930,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_13392,c_13926]) ).

tcf(c_13951,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),X1) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(member_int(X0,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),cOMBC_int_int_bool(ord_less_int,X1)))) ),
    inference(demodulation,[status(thm)],[c_1701,c_228]) ).

tcf(c_13995,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X2,X0))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X1),sK28(X2,X1)))
      | ~ hBOOL(hAPP_int_bool(X2,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_1555,c_1720]) ).

tcf(c_14104,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0))),
    inference(demodulation,[status(thm)],[c_1226,c_232,c_238,c_241,c_373,c_408,c_11295]) ).

tcf(c_14189,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_903,c_232,c_13390,c_13391]) ).

tcf(c_14190,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))),
    inference(demodulation,[status(thm)],[c_862,c_232,c_238,c_241]) ).

tcf(c_14195,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),
    inference(demodulation,[status(thm)],[c_643,c_232,c_238,c_241,c_13926]) ).

tcf(c_14196,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),
    inference(demodulation,[status(thm)],[c_642,c_232,c_238,c_241,c_13926]) ).

tcf(c_14225,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),X1)),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))),X0),
    inference(demodulation,[status(thm)],[c_406,c_232,c_241,c_1013]) ).

tcf(c_14226,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),
    inference(demodulation,[status(thm)],[c_358,c_232,c_238,c_241,c_13926]) ).

tcf(c_14233,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_2632,c_232]) ).

tcf(c_14240,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2633,c_232]) ).

tcf(c_14247,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_2628,c_232]) ).

tcf(c_14254,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_2629,c_232]) ).

tcf(c_14294,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(one_one_int),sK31(X0,X1)))) ),
    inference(demodulation,[status(thm)],[c_1564,c_241]) ).

tcf(c_14654,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),
    inference(demodulation,[status(thm)],[c_651,c_232,c_238,c_241,c_1720,c_13926]) ).

tcf(c_14655,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),zero_zero_real)),
    inference(demodulation,[status(thm)],[c_650,c_232,c_238,c_241,c_13926]) ).

tcf(c_14656,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_588,c_1720]) ).

tcf(c_14669,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))) ),
    inference(demodulation,[status(thm)],[c_587,c_1720]) ).

tcf(c_14792,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)) = hAPP_real_real(plus_plus_real(X0),X0),
    inference(demodulation,[status(thm)],[c_420,c_232,c_238,c_241,c_373,c_408,c_11295]) ).

tcf(c_14793,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(demodulation,[status(thm)],[c_418,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_14796,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(X0),X0),
    inference(demodulation,[status(thm)],[c_149,c_232,c_238,c_241,c_13926]) ).

tcf(c_14804,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = hAPP_nat_nat(times_times_nat(X0),X0),
    inference(demodulation,[status(thm)],[c_99,c_232,c_238,c_241,c_13926]) ).

tcf(c_14806,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = hAPP_real_real(times_times_real(X0),X0),
    inference(demodulation,[status(thm)],[c_98,c_232,c_238,c_241,c_13926]) ).

tcf(c_14808,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = hAPP_int_int(times_times_int(X0),X0),
    inference(demodulation,[status(thm)],[c_97,c_232,c_238,c_241,c_13926]) ).

tcf(c_14810,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(div_mod_int(X0),X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(demodulation,[status(thm)],[c_5596,c_1720]) ).

tcf(c_14846,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X1),sK29(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(demodulation,[status(thm)],[c_1559,c_1720]) ).

tcf(c_14881,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0)) = one_one_int,
    inference(demodulation,[status(thm)],[c_836,c_232,c_238,c_241,c_13926]) ).

tcf(c_14882,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0)) = one_one_real,
    inference(demodulation,[status(thm)],[c_835,c_232,c_238,c_241,c_13926]) ).

tcf(c_14895,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)) != hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)) ) ),
    inference(demodulation,[status(thm)],[c_249,c_232]) ).

tcf(c_14928,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(one_one_int),one_one_int)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)),
    inference(demodulation,[status(thm)],[c_891,c_232,c_1021]) ).

tcf(c_14929,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1))),
    inference(demodulation,[status(thm)],[c_890,c_232]) ).

tcf(c_14940,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)))),
    inference(demodulation,[status(thm)],[c_697,c_232,c_238,c_241,c_13926]) ).

tcf(c_14941,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)))),
    inference(demodulation,[status(thm)],[c_696,c_232,c_238,c_241,c_13926]) ).

tcf(c_14942,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))),
    inference(demodulation,[status(thm)],[c_391,c_232]) ).

tcf(c_14948,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(one_one_int),sK32(X0,X1)))) ),
    inference(demodulation,[status(thm)],[c_1568,c_241]) ).

tcf(c_14993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(multInv(X3,X0)),X1)),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3)) ),
    inference(demodulation,[status(thm)],[c_3435,c_211,c_217]) ).

tcf(c_15008,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))
      | ( X0 = zero_zero_real ) ),
    inference(demodulation,[status(thm)],[c_3613,c_232,c_238,c_241,c_13926]) ).

tcf(c_15059,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0))) = hAPP_nat_nat(minus_minus_nat(X2),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_1305,c_242,c_11972]) ).

tcf(c_15077,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_3297,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0))),X2)),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_3067,c_1012]) ).

tcf(c_15133,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))
      | ( X0 = pls )
      | ~ is_int(X0) ),
    inference(demodulation,[status(thm)],[c_654,c_232,c_238,c_241,c_13926]) ).

tcf(c_15143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X4),X3)),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X2))) ),
    inference(demodulation,[status(thm)],[c_538,c_232]) ).

tcf(c_15153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X4)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4)))) ),
    inference(demodulation,[status(thm)],[c_537,c_232]) ).

tcf(c_15163,plain,
    ! [X0: $i] : hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)),
    inference(demodulation,[status(thm)],[c_411,c_212,c_232,c_238,c_241]) ).

tcf(c_15164,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X0),X0)),
    inference(demodulation,[status(thm)],[c_410,c_213,c_232,c_238,c_241]) ).

tcf(c_15165,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_409,c_211,c_232,c_238,c_241]) ).

tcf(c_15184,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2))) ),
    inference(demodulation,[status(thm)],[c_5579,c_1720]) ).

tcf(c_15233,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1),X0))
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(demodulation,[status(thm)],[c_3315,c_232,c_238,c_241,c_13926]) ).

tcf(c_15254,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1))),zero_zero_real)) ),
    inference(demodulation,[status(thm)],[c_3257,c_232,c_238,c_241,c_13926]) ).

tcf(c_15333,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1),X2)) ),
    inference(demodulation,[status(thm)],[c_944,c_232,c_238,c_241,c_13926]) ).

tcf(c_15395,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X1)),
    inference(demodulation,[status(thm)],[c_105,c_146,c_232,c_238,c_241,c_13926]) ).

tcf(c_15396,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(X1),X1)),
    inference(demodulation,[status(thm)],[c_104,c_145,c_232,c_238,c_241,c_13926]) ).

tcf(c_15397,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(X1),X1)),
    inference(demodulation,[status(thm)],[c_103,c_144,c_232,c_238,c_241,c_13926]) ).

tcf(c_15398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(div_mod_int(X3),X2))),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_1671,c_1720]) ).

tcf(c_15419,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)))) ),
    inference(demodulation,[status(thm)],[c_723,c_232,c_238,c_241,c_1720,c_13926]) ).

tcf(c_15481,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(X1,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_873,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(div_mod_int(X3),X2))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_1669,c_1720]) ).

tcf(c_15526,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(number_number_of_int(X0)),number_number_of_int(X1))),
    inference(demodulation,[status(thm)],[c_1646,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X3),hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_int_bool(X0,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(plus_plus_int(X1),sK25(X0,X1)))) ),
    inference(demodulation,[status(thm)],[c_1506,c_241]) ).

tcf(c_15567,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1),X2)) ),
    inference(demodulation,[status(thm)],[c_720,c_232,c_238,c_241,c_13926]) ).

tcf(c_15577,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),multInv(X0,X2)),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1530,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15627,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X0)),X1))
      | ( X1 = zero_zero_nat )
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(demodulation,[status(thm)],[c_943,c_232,c_238,c_241,c_13926]) ).

tcf(c_15640,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X1),X0)),hAPP_int_int(div_mod_int(X2),X0)),hAPP_int_int(times_times_int(X1),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_3299,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15695,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ( X0 = one_one_int )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
    inference(demodulation,[status(thm)],[c_721,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15781,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1535,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15822,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(multInv(X0,multInv(X0,X1)),X1),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1534,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15835,plain,
    hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_82,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15836,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),multInv(X0,X1)),one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1544,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15866,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = pls )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = one_one_int ) ),
    inference(demodulation,[status(thm)],[c_2846,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X3),multInv(X0,X1)),hAPP_int_int(times_times_int(X3),multInv(X0,X2))),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1532,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15883,plain,
    hBOOL(hAPP_int_bool(quadRes(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),number_number_of_int(min))),
    inference(demodulation,[status(thm)],[c_2597,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15904,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK11),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_458,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15905,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_457,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15906,plain,
    hBOOL(hAPP_int_bool(zcong(s1,sK10),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_454,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15907,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_453,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15908,plain,
    hBOOL(hAPP_int_bool(zcong(s1,s),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_450,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15909,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_449,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15910,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_426,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15911,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_81,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15912,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) != hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) ) ),
    inference(demodulation,[status(thm)],[c_5747,c_232,c_238,c_241,c_13926]) ).

tcf(c_15920,plain,
    legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = one_one_int,
    inference(demodulation,[status(thm)],[c_736,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15922,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))),
    inference(demodulation,[status(thm)],[c_681,c_232,c_238,c_241,c_13926]) ).

tcf(c_15923,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))),
    inference(demodulation,[status(thm)],[c_680,c_232,c_238,c_241,c_13926]) ).

tcf(c_15924,plain,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),
    inference(demodulation,[status(thm)],[c_84,c_211,c_217,c_220,c_232,c_238,c_241,c_368,c_371,c_407,c_11296]) ).

tcf(c_15926,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != pls )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != one_one_int ) ),
    inference(demodulation,[status(thm)],[c_2844,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15934,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))),
    inference(demodulation,[status(thm)],[c_689,c_232,c_238,c_241,c_1720,c_13926]) ).

tcf(c_15935,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real)),
    inference(demodulation,[status(thm)],[c_688,c_232,c_238,c_241,c_13926]) ).

tcf(c_15936,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_283,c_124,c_232,c_238,c_241,c_13926]) ).

tcf(c_15937,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_282,c_123,c_232,c_238,c_241,c_13926]) ).

tcf(c_15938,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1)) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_281,c_122,c_232,c_238,c_241,c_13926]) ).

tcf(c_15939,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))) = hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_93,c_232,c_238,c_241,c_13926]) ).

tcf(c_15940,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(s),s)),number_number_of_int(min)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),
    inference(demodulation,[status(thm)],[c_875,c_232,c_238,c_241,c_13926,c_14808]) ).

tcf(c_15941,plain,
    ! [X0: $i] :
      ( ( wset(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0) = d22set(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) )
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(demodulation,[status(thm)],[c_3001,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15948,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(number_number_of_int(min)),X0) = hAPP_nat_int(power_power_int(number_number_of_int(min)),X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),X0),hAPP_nat_int(power_power_int(number_number_of_int(min)),X1)),X2)) ),
    inference(demodulation,[status(thm)],[c_872,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_15958,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real ) ),
    inference(demodulation,[status(thm)],[c_3247,c_232,c_238,c_241,c_13926]) ).

tcf(c_15965,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real ) ),
    inference(demodulation,[status(thm)],[c_3245,c_232,c_238,c_241,c_13926]) ).

tcf(c_15972,plain,
    hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_429,c_211,c_217,c_220,c_232,c_238,c_241,c_368,c_371,c_407,c_11296]) ).

tcf(c_15973,plain,
    hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(demodulation,[status(thm)],[c_15924,c_15972]) ).

tcf(c_15974,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) ),
    inference(demodulation,[status(thm)],[c_5746,c_232,c_238,c_241,c_13926]) ).

tcf(c_16005,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X0 = zero_zero_real ) ),
    inference(demodulation,[status(thm)],[c_3621,c_232,c_238,c_241,c_13926]) ).

tcf(c_16012,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X0 = zero_zero_real ) ),
    inference(demodulation,[status(thm)],[c_3619,c_232,c_238,c_241,c_13926]) ).

tcf(c_16037,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2953,c_232,c_238,c_241,c_371,c_407,c_11296,c_12842]) ).

tcf(c_16044,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(multInv(X0,X1)),multInv(X0,multInv(X0,X1)))),X1),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1541,c_211,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16057,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real)) ),
    inference(demodulation,[status(thm)],[c_3251,c_232,c_238,c_241,c_13926]) ).

tcf(c_16064,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real)) ),
    inference(demodulation,[status(thm)],[c_3249,c_232,c_238,c_241,c_13926]) ).

tcf(c_16071,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)),
    inference(demodulation,[status(thm)],[c_986,c_232,c_238,c_241,c_13926]) ).

tcf(c_16072,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(X0),X1)),
    inference(demodulation,[status(thm)],[c_912,c_232,c_238,c_241,c_13926]) ).

tcf(c_16073,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) ) ),
    inference(demodulation,[status(thm)],[c_3456,c_232,c_238,c_241,c_371,c_407,c_11296,c_12842]) ).

tcf(c_16080,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(multInv(X0,multInv(X0,X1)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(multInv(X0,X1)),multInv(X0,multInv(X0,X1))))),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(demodulation,[status(thm)],[c_1542,c_211,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16093,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != pls ) ),
    inference(demodulation,[status(thm)],[c_661,c_232,c_238,c_241,c_13926]) ).

tcf(c_16106,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != pls ) ),
    inference(demodulation,[status(thm)],[c_660,c_232,c_238,c_241,c_13926]) ).

tcf(c_16119,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X2,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X0))
      | hBOOL(hAPP_int_bool(zcong(X1,X2),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(multInv(X0,X1),multInv(X0,X2)),X0)) ),
    inference(demodulation,[status(thm)],[c_1533,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16138,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(quadRes(X2),X1))
      | hBOOL(hAPP_int_bool(zcong(X1,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2)) ),
    inference(demodulation,[status(thm)],[c_1522,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16157,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(demodulation,[status(thm)],[c_694,c_232,c_238,c_241,c_13926]) ).

tcf(c_16170,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(demodulation,[status(thm)],[c_693,c_232,c_238,c_241,c_13926]) ).

tcf(c_16183,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))) ),
    inference(demodulation,[status(thm)],[c_687,c_232,c_238,c_241,c_1720,c_13926]) ).

tcf(c_16196,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = pls )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))) ),
    inference(demodulation,[status(thm)],[c_686,c_232,c_238,c_241,c_1720,c_13926]) ).

tcf(c_16209,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) ),
    inference(demodulation,[status(thm)],[c_646,c_232,c_238,c_241,c_13926]) ).

tcf(c_16219,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) ),
    inference(demodulation,[status(thm)],[c_644,c_232,c_238,c_241,c_13926]) ).

tcf(c_16229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,pls),X3))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3))
      | ~ hBOOL(hAPP_int_bool(zprime,X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),multInv(X3,X1)))),X3)) ),
    inference(demodulation,[status(thm)],[c_1538,c_211,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16245,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0))
      | ( hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) != hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) ) ),
    inference(demodulation,[status(thm)],[c_647,c_232,c_238,c_241,c_13926]) ).

tcf(c_16258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X3,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X2))
      | hBOOL(hAPP_int_bool(zcong(X3,hAPP_int_int(times_times_int(X1),multInv(X2,X0))),X2))
      | ~ hBOOL(hAPP_int_bool(zprime,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,hAPP_int_int(times_times_int(X1),multInv(X2,X3))),X2)) ),
    inference(demodulation,[status(thm)],[c_1539,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5)))
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X2) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X4)),X5) ) ),
    inference(demodulation,[status(thm)],[c_863,c_1720]) ).

tcf(c_16313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(X2,hAPP_int_int(times_times_int(X3),multInv(X1,X0))),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(multInv(X1,X0)),X2)),hAPP_int_int(times_times_int(multInv(X1,X0)),X3)),X1)) ),
    inference(demodulation,[status(thm)],[c_1537,c_211,c_217,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16329,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK13),sK13),number_number_of_int(min)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_734,c_220,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926,c_14808]) ).

tcf(c_16330,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(s),s),number_number_of_int(min)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_719,c_220,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926,c_14808]) ).

tcf(c_16331,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(s1),s1),number_number_of_int(min)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_460,c_220,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926,c_14808]) ).

tcf(c_16332,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ( hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) != hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) ) ),
    inference(demodulation,[status(thm)],[c_649,c_232,c_238,c_241,c_13926]) ).

tcf(c_16351,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_427,c_220,c_232,c_238,c_241,c_371,c_407,c_1720,c_11296,c_13926,c_14808]) ).

tcf(c_16352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X3,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(X2,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | hBOOL(hAPP_int_bool(zcong(X2,X3),X1))
      | ~ hBOOL(hAPP_int_bool(zprime,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),multInv(X1,X2)),hAPP_int_int(times_times_int(X0),multInv(X1,X3))),X1)) ),
    inference(demodulation,[status(thm)],[c_1540,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16375,plain,
    hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK9),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),
    inference(demodulation,[status(thm)],[c_112,c_211,c_217,c_220,c_232,c_238,c_241,c_368,c_371,c_407,c_11296,c_13926,c_14808]) ).

tcf(c_16376,plain,
    hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_83,c_211,c_217,c_220,c_232,c_238,c_241,c_368,c_371,c_407,c_11296,c_13926,c_14808,c_15972]) ).

tcf(c_16377,plain,
    hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK9),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_16375,c_16376]) ).

tcf(c_16378,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_16351,c_16376]) ).

tcf(c_16379,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(s),s)),number_number_of_int(min)) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_15940,c_16376]) ).

tcf(c_16380,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(inv(X0,X2),wset(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(member_int(X2,wset(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))))))))),X0)) ),
    inference(demodulation,[status(thm)],[c_1545,c_232,c_238,c_241]) ).

tcf(c_16396,plain,
    ! [X0: $i,X1: $i] :
      ( ( inv(X0,inv(X0,X1)) = X1 )
      | ~ is_int(X1)
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))))))))),X0)) ),
    inference(demodulation,[status(thm)],[c_1521,c_232,c_238,c_241]) ).

tcf(c_16415,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))))))) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
    inference(demodulation,[status(thm)],[c_412,c_122,c_232,c_238,c_241,c_13926,c_14804]) ).

tcf(c_16416,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(X1),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(demodulation,[status(thm)],[c_2957,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16423,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0))),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(demodulation,[status(thm)],[c_2989,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16430,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(s),s),hAPP_int_int(times_times_int(s1),s1)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
    inference(demodulation,[status(thm)],[c_447,c_220,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926,c_14808]) ).

tcf(c_16431,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))),
    inference(demodulation,[status(thm)],[c_1723,c_220,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926]) ).

tcf(c_16432,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X1,wset(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(zprime,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | ~ hBOOL(member_int(inv(X0,X1),wset(X2,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))))))))),X0)) ),
    inference(demodulation,[status(thm)],[c_1546,c_232,c_238,c_241]) ).

tcf(c_16454,plain,
    ! [X0: $i] :
      ( ( legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),X0))) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),X0)))) ),
    inference(demodulation,[status(thm)],[c_3311,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16461,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(X1),X0)))) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X1),X0)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_922,c_211,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926]) ).

tcf(c_16462,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(X0),X1))) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_921,c_211,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926]) ).

tcf(c_16463,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X1))) = hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X0),X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_920,c_213,c_232,c_238,c_241,c_373,c_408,c_11295,c_13926]) ).

tcf(c_16464,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X1)))) = hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_89,c_213,c_232,c_234,c_238,c_241,c_373,c_408,c_11295,c_13926]) ).

tcf(c_16465,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),hAPP_nat_nat(times_times_nat(X0),X1)))) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_88,c_212,c_232,c_233,c_238,c_241,c_13926]) ).

tcf(c_16466,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(X0),X1)))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_87,c_211,c_232,c_238,c_241,c_371,c_407,c_11296,c_13926]) ).

tcf(c_16467,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))))))))),X0))
      | ( hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = X0 )
      | ( number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))) = X0 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(demodulation,[status(thm)],[c_428,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16483,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
    inference(demodulation,[status(thm)],[c_431,c_213,c_232,c_238,c_241,c_373,c_408,c_11295,c_13926]) ).

tcf(c_16484,plain,
    ! [X0: $i] :
      ( ( X0 = sK10 )
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(s1,X0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))) ),
    inference(demodulation,[status(thm)],[c_455,c_220,c_232,c_238,c_241,c_371,c_407,c_11296]) ).

tcf(c_16500,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))),hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),X1))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))) = hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),
    inference(demodulation,[status(thm)],[c_923,c_211,c_232,c_238,c_241,c_13926]) ).

tcf(c_16501,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),X1))))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),
    inference(demodulation,[status(thm)],[c_86,c_211,c_232,c_238,c_241,c_320,c_13926]) ).

tcf(c_18160,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5551]) ).

tcf(c_18161,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_18160]) ).

tcf(c_18162,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552]) ).

tcf(c_18163,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_18162]) ).

tcf(c_18164,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_172,c_5551]) ).

tcf(c_18165,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(renaming,[status(thm)],[c_18164]) ).

tcf(c_18166,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_171,c_5552]) ).

tcf(c_18167,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(renaming,[status(thm)],[c_18166]) ).

tcf(c_18172,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_142,c_5551]) ).

tcf(c_18173,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_18172]) ).

tcf(c_18174,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_141,c_5552]) ).

tcf(c_18175,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_18174]) ).

tcf(c_18188,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_168,c_5551]) ).

tcf(c_18189,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_18188]) ).

tcf(c_18190,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_167,c_5552]) ).

tcf(c_18191,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_18190]) ).

tcf(c_18196,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_196,c_5551]) ).

tcf(c_18197,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(renaming,[status(thm)],[c_18196]) ).

tcf(c_18198,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_195,c_5552]) ).

tcf(c_18199,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(renaming,[status(thm)],[c_18198]) ).

tcf(c_18290,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1332]) ).

tcf(c_18364,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11687,c_13139]) ).

tcf(c_18365,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(renaming,[status(thm)],[c_18364]) ).

tcf(c_18366,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11694,c_13132]) ).

tcf(c_18372,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11709,c_13167]) ).

tcf(c_18373,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(renaming,[status(thm)],[c_18372]) ).

tcf(c_18374,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11716,c_13160]) ).

tcf(c_18376,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5551,c_13434]) ).

tcf(c_18377,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18376]) ).

tcf(c_18378,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552,c_13441]) ).

tcf(c_18379,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18378]) ).

tcf(c_18384,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5551,c_13468]) ).

tcf(c_18385,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18384]) ).

tcf(c_18386,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552,c_13475]) ).

tcf(c_18387,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18386]) ).

tcf(c_18392,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5551,c_14233]) ).

tcf(c_18393,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18392]) ).

tcf(c_18394,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552,c_14240]) ).

tcf(c_18395,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_18394]) ).

tcf(c_18442,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_115,c_5551]) ).

tcf(c_18443,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_18442]) ).

tcf(c_18612,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X2),X0)),hAPP_int_int(plus_plus_int(X2),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_174,c_5552]) ).

tcf(c_18613,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2))) ),
    inference(renaming,[status(thm)],[c_18612]) ).

tcf(c_20863,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_18443,c_18161]) ).

tcf(c_20866,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_120,c_18163]) ).

tcf(c_20867,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ( X1 = X0 )
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_121,c_18163]) ).

tcf(c_20868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_143,c_18163]) ).

tcf(c_20870,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X2),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_528,c_18163]) ).

tcf(c_20871,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_926,c_18161]) ).

tcf(c_20872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1079,c_18163]) ).

tcf(c_20873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X2)),hAPP_int_int(times_times_int(X1),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1082,c_18163]) ).

tcf(c_20874,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(bin_hyper_res,[status(thm)],[c_1084,c_18163]) ).

tcf(c_20875,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(bin_hyper_res,[status(thm)],[c_1086,c_18163]) ).

tcf(c_20876,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_1089,c_18163]) ).

tcf(c_20877,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(times_times_int(X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_1095,c_18163]) ).

tcf(c_20878,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(X0,sK28(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1554,c_18163]) ).

tcf(c_20879,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | is_int(sK28(X0,X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1556,c_18163]) ).

tcf(c_20880,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(X0,sK31(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1565,c_18163]) ).

tcf(c_20881,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK31(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1566,c_18163]) ).

tcf(c_20882,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | is_int(sK31(X0,X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_1567,c_18163]) ).

tcf(c_20883,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X0,d22set(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_1581,c_18163]) ).

tcf(c_20884,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_5591,c_18290]) ).

tcf(c_20885,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X1),sK28(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_13995,c_18163]) ).

tcf(c_20886,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) ),
    inference(bin_hyper_res,[status(thm)],[c_16209,c_18161]) ).

tcf(c_32037,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552]) ).

tcf(c_32038,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_32037]) ).

tcf(c_34728,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_20866,c_32038]) ).

tcf(c_34729,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ( X1 = X0 )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(bin_hyper_res,[status(thm)],[c_20867,c_32038]) ).

tcf(c_34730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X2),X1)),hAPP_int_int(times_times_int(X0),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_20872,c_32038]) ).

tcf(c_34731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(bin_hyper_res,[status(thm)],[c_20873,c_32038]) ).

tcf(c_45836,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5551]) ).

tcf(c_45837,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_45836]) ).

tcf(c_45838,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_5552]) ).

tcf(c_45839,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(renaming,[status(thm)],[c_45838]) ).

tcf(c_45840,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18165]) ).

tcf(c_45841,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(renaming,[status(thm)],[c_45840]) ).

tcf(c_45842,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18167]) ).

tcf(c_45843,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(renaming,[status(thm)],[c_45842]) ).

tcf(c_45848,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18173]) ).

tcf(c_45849,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_45848]) ).

tcf(c_45850,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18175]) ).

tcf(c_45851,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(renaming,[status(thm)],[c_45850]) ).

tcf(c_45864,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18189]) ).

tcf(c_45865,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_45864]) ).

tcf(c_45866,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18191]) ).

tcf(c_45867,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_45866]) ).

tcf(c_45872,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18197]) ).

tcf(c_45873,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(renaming,[status(thm)],[c_45872]) ).

tcf(c_45874,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18199]) ).

tcf(c_45875,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
    inference(renaming,[status(thm)],[c_45874]) ).

tcf(c_45876,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2680]) ).

tcf(c_45877,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_45876]) ).

tcf(c_45878,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2681]) ).

tcf(c_45888,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11709]) ).

tcf(c_45889,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(renaming,[status(thm)],[c_45888]) ).

tcf(c_45890,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11716]) ).

tcf(c_45892,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_2712]) ).

tcf(c_45893,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_45892]) ).

tcf(c_45894,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_2713]) ).

tcf(c_45896,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11687]) ).

tcf(c_45897,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(renaming,[status(thm)],[c_45896]) ).

tcf(c_45898,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_11694]) ).

tcf(c_45900,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_2728]) ).

tcf(c_45901,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_45900]) ).

tcf(c_45902,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_2729]) ).

tcf(c_45912,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2744]) ).

tcf(c_45913,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_45912]) ).

tcf(c_45914,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2745]) ).

tcf(c_45916,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2748]) ).

tcf(c_45917,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(renaming,[status(thm)],[c_45916]) ).

tcf(c_45918,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2749]) ).

tcf(c_45948,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2812]) ).

tcf(c_45949,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(renaming,[status(thm)],[c_45948]) ).

tcf(c_45950,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2813]) ).

tcf(c_45976,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_11591]) ).

tcf(c_45977,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_45976]) ).

tcf(c_45978,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_11598]) ).

tcf(c_45980,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_11637]) ).

tcf(c_45981,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(renaming,[status(thm)],[c_45980]) ).

tcf(c_45982,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_11644]) ).

tcf(c_45984,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_12078]) ).

tcf(c_45985,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),X1))) ),
    inference(renaming,[status(thm)],[c_45984]) ).

tcf(c_45986,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_12071]) ).

tcf(c_45988,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12101]) ).

tcf(c_45989,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_45988]) ).

tcf(c_45990,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12108]) ).

tcf(c_45992,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12123]) ).

tcf(c_45993,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_45992]) ).

tcf(c_45994,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12130]) ).

tcf(c_45996,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12199]) ).

tcf(c_45997,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_45996]) ).

tcf(c_45998,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12206]) ).

tcf(c_46000,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12213]) ).

tcf(c_46001,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(renaming,[status(thm)],[c_46000]) ).

tcf(c_46002,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12220]) ).

tcf(c_46004,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12733]) ).

tcf(c_46005,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46004]) ).

tcf(c_46006,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12740]) ).

tcf(c_46008,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12747]) ).

tcf(c_46009,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46008]) ).

tcf(c_46010,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12754]) ).

tcf(c_46012,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12761]) ).

tcf(c_46013,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46012]) ).

tcf(c_46014,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12768]) ).

tcf(c_46016,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12775]) ).

tcf(c_46017,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46016]) ).

tcf(c_46018,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(prop_impl_just,[status(thm)],[c_12782]) ).

tcf(c_46020,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12843]) ).

tcf(c_46021,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46020]) ).

tcf(c_46022,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12850]) ).

tcf(c_46024,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12857]) ).

tcf(c_46025,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46024]) ).

tcf(c_46026,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12864]) ).

tcf(c_46028,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12871]) ).

tcf(c_46029,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46028]) ).

tcf(c_46030,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12878]) ).

tcf(c_46032,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12885]) ).

tcf(c_46033,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(renaming,[status(thm)],[c_46032]) ).

tcf(c_46034,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_12892]) ).

tcf(c_46036,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_13125]) ).

tcf(c_46037,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) ),
    inference(renaming,[status(thm)],[c_46036]) ).

tcf(c_46038,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_13118]) ).

tcf(c_46040,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_18365]) ).

tcf(c_46041,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(renaming,[status(thm)],[c_46040]) ).

tcf(c_46042,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_18366]) ).

tcf(c_46044,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_13153]) ).

tcf(c_46045,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) ),
    inference(renaming,[status(thm)],[c_46044]) ).

tcf(c_46046,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_13146]) ).

tcf(c_46048,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_18373]) ).

tcf(c_46049,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(renaming,[status(thm)],[c_46048]) ).

tcf(c_46050,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_18374]) ).

tcf(c_46052,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18377]) ).

tcf(c_46053,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46052]) ).

tcf(c_46054,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18379]) ).

tcf(c_46055,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46054]) ).

tcf(c_46056,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_13448]) ).

tcf(c_46057,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_46056]) ).

tcf(c_46058,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_13455]) ).

tcf(c_46060,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18385]) ).

tcf(c_46061,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46060]) ).

tcf(c_46062,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18387]) ).

tcf(c_46063,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46062]) ).

tcf(c_46064,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_13482]) ).

tcf(c_46065,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(renaming,[status(thm)],[c_46064]) ).

tcf(c_46066,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_13489]) ).

tcf(c_46068,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18393]) ).

tcf(c_46069,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46068]) ).

tcf(c_46070,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_18395]) ).

tcf(c_46071,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46070]) ).

tcf(c_46072,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_14247]) ).

tcf(c_46073,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(renaming,[status(thm)],[c_46072]) ).

tcf(c_46074,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_14254]) ).

tcf(c_46076,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != one_one_int )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != pls ) ),
    inference(prop_impl_just,[status(thm)],[c_15926]) ).

tcf(c_46077,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != pls )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) != one_one_int ) ),
    inference(renaming,[status(thm)],[c_46076]) ).

tcf(c_46078,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = one_one_int )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = pls ) ),
    inference(prop_impl_just,[status(thm)],[c_15866]) ).

tcf(c_46079,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = pls )
      | ( hAPP_int_int(div_mod_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = one_one_int ) ),
    inference(renaming,[status(thm)],[c_46078]) ).

tcf(c_46104,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),X0)),X1) = pls )
      | ~ is_int(X0) ),
    inference(prop_impl_just,[status(thm)],[c_6365]) ).

tcf(c_46106,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(X0),X1)) = X0 )
      | ~ is_int(X0) ),
    inference(prop_impl_just,[status(thm)],[c_11468]) ).

tcf(c_46108,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2908]) ).

tcf(c_46109,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(renaming,[status(thm)],[c_46108]) ).

tcf(c_46112,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_20863]) ).

tcf(c_46130,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_11870]) ).

tcf(c_46142,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_2949]) ).

tcf(c_46144,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X0),hAPP_int_int(div_mod_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_11877]) ).

tcf(c_46146,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_12945]) ).

tcf(c_46148,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(number_number_of_int(X1)),number_number_of_int(X0)))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_16037]) ).

tcf(c_46150,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(X1),X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_16416]) ).

tcf(c_46162,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2975]) ).

tcf(c_46164,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2981]) ).

tcf(c_46166,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2983]) ).

tcf(c_46168,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2985]) ).

tcf(c_46172,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0))),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_16423]) ).

tcf(c_46174,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2992]) ).

tcf(c_46175,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = zero_zero_real ) ),
    inference(renaming,[status(thm)],[c_46174]) ).

tcf(c_46176,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2994]) ).

tcf(c_46177,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat ) ),
    inference(renaming,[status(thm)],[c_46176]) ).

tcf(c_46178,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = pls )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(prop_impl_just,[status(thm)],[c_2996]) ).

tcf(c_46179,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = pls ) ),
    inference(renaming,[status(thm)],[c_46178]) ).

tcf(c_46184,plain,
    ! [X0: $i] :
      ( ( wset(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0) = d22set(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) )
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_15941]) ).

tcf(c_46196,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),sK26(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_11564]) ).

tcf(c_46214,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),X2)),hAPP_nat_nat(power_power_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1330,c_529]) ).

tcf(c_46252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0))),X2)),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_15126]) ).

tcf(c_46258,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_15974]) ).

tcf(c_46259,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))) ),
    inference(renaming,[status(thm)],[c_46258]) ).

tcf(c_46286,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_2507]) ).

tcf(c_46287,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(renaming,[status(thm)],[c_46286]) ).

tcf(c_46324,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_int(power_power_int(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_13824]) ).

tcf(c_46326,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_real(power_power_real(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_13831]) ).

tcf(c_46328,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),one_one_nat))) = hAPP_nat_nat(power_power_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_13838]) ).

tcf(c_46382,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(power_power_nat(X2),X1))) ),
    inference(prop_impl_just,[status(thm)],[c_5744]) ).

tcf(c_46398,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_2928]) ).

tcf(c_46400,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3223]) ).

tcf(c_46404,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X1,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3227]) ).

tcf(c_46406,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK27(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3229]) ).

tcf(c_46408,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X1,sK27(X1,X0)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3233]) ).

tcf(c_46410,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3237]) ).

tcf(c_46412,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(number_number_of_int(min)),X0) = hAPP_int_int(minus_minus_int(X0),one_one_int) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3239]) ).

tcf(c_46414,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),sK27(X1,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_11656]) ).

tcf(c_46416,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),hAPP_int_int(div_mod_int(X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_11820]) ).

tcf(c_46418,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_3241]) ).

tcf(c_46426,plain,
    ( ( number_number_of_int(hAPP_int_int(times_times_int(min),min)) = one_one_int )
    | ~ is_int(number_number_of_int(min)) ),
    inference(prop_impl_just,[status(thm)],[c_11495]) ).

tcf(c_46444,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_18613]) ).

tcf(c_46445,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X0),X2))) ),
    inference(renaming,[status(thm)],[c_46444]) ).

tcf(c_46446,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(X1)) != zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_2978]) ).

tcf(c_46448,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),number_number_of_nat(X1)) != zero_zero_nat ) ),
    inference(prop_impl_just,[status(thm)],[c_2980]) ).

tcf(c_46464,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0))
      | ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_15077]) ).

tcf(c_46465,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(renaming,[status(thm)],[c_46464]) ).

tcf(c_46476,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK15(X0,X1)),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1),X0))
      | ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
    inference(prop_impl_just,[status(thm)],[c_15233]) ).

tcf(c_46504,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(prop_impl_just,[status(thm)],[c_5741]) ).

tcf(c_46506,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(prop_impl_just,[status(thm)],[c_5740]) ).

tcf(c_46560,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(prop_impl_just,[status(thm)],[c_1385,c_1393]) ).

tcf(c_46594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(multInv(X3,X0)),X1)),hAPP_int_int(times_times_int(multInv(X3,X0)),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),X2),X3)) ),
    inference(prop_impl_just,[status(thm)],[c_14993]) ).

tcf(c_46610,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_16073]) ).

tcf(c_46611,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X1)))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0))),number_number_of_int(X1)))),one_one_int) = hAPP_int_int(div_mod_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) ) ),
    inference(renaming,[status(thm)],[c_46610]) ).

tcf(c_46638,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK39(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK38(X0,X1,X2))) = X2 )
      | sP3(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_12963]) ).

tcf(c_46639,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK39(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK38(X0,X1,X2))) = X2 ) ),
    inference(renaming,[status(thm)],[c_46638]) ).

tcf(c_46692,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),sK39(X1,X0,X2)))
      | sP3(X1,X0,X2) ),
    inference(prop_impl_just,[status(thm)],[c_11429]) ).

tcf(c_46693,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),sK39(X1,X0,X2))) ),
    inference(renaming,[status(thm)],[c_46692]) ).

tcf(c_46750,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_15008]) ).

tcf(c_46752,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1))),zero_zero_real))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_15254]) ).

tcf(c_46753,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),X1))),zero_zero_real)) ),
    inference(renaming,[status(thm)],[c_46752]) ).

tcf(c_46754,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real )
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_15965]) ).

tcf(c_46755,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real ) ),
    inference(renaming,[status(thm)],[c_46754]) ).

tcf(c_46756,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_16005]) ).

tcf(c_46758,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_16012]) ).

tcf(c_46760,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real))
      | ( X0 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_16064]) ).

tcf(c_46761,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real)) ),
    inference(renaming,[status(thm)],[c_46760]) ).

tcf(c_46788,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real )
      | ( X1 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_15958]) ).

tcf(c_46789,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) != zero_zero_real ) ),
    inference(renaming,[status(thm)],[c_46788]) ).

tcf(c_46790,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real))
      | ( X1 = zero_zero_real ) ),
    inference(prop_impl_just,[status(thm)],[c_16057]) ).

tcf(c_46791,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_real)) ),
    inference(renaming,[status(thm)],[c_46790]) ).

tcf(c_46854,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) != hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) )
      | ( X0 = X1 ) ),
    inference(prop_impl_just,[status(thm)],[c_15912]) ).

tcf(c_46855,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) != hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) ) ),
    inference(renaming,[status(thm)],[c_46854]) ).

tcf(c_47012,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0))
      | hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X1),X0)),hAPP_int_int(div_mod_int(X2),X0)),hAPP_int_int(times_times_int(X1),X2)),X0)) ),
    inference(prop_impl_just,[status(thm)],[c_15640]) ).

tcf(c_47013,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(div_mod_int(X1),X0)),hAPP_int_int(div_mod_int(X2),X0)),hAPP_int_int(times_times_int(X1),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0)) ),
    inference(renaming,[status(thm)],[c_47012]) ).

tcf(c_47086,plain,
    ! [X0: $i] :
      ( ( legendre(number_number_of_int(min),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),X0))) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(zprime,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),X0)))) ),
    inference(prop_impl_just,[status(thm)],[c_16454]) ).

tcf(c_48529,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(bin_hyper_res,[status(thm)],[c_34728,c_45837]) ).

tcf(c_59634,definition,
    iPr_def_10 = plus_plus_nat(one_one_nat),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_59635,definition,
    iPr_def_11 = hAPP_nat_nat(iPr_def_10,one_one_nat),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_59636,definition,
    iPr_def_12 = plus_plus_int(one_one_int),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_59637,definition,
    iPr_def_13 = times_times_int(m),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_59638,definition,
    iPr_def_14 = hAPP_int_int(iPr_def_12,one_one_int),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_59639,definition,
    iPr_def_15 = hAPP_int_int(iPr_def_12,iPr_def_14),
    introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).

tcf(c_59640,definition,
    iPr_def_16 = hAPP_int_int(iPr_def_12,iPr_def_15),
    introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).

tcf(c_59641,definition,
    iPr_def_17 = hAPP_int_int(iPr_def_13,iPr_def_16),
    introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).

tcf(c_59642,definition,
    iPr_def_18 = hAPP_int_int(iPr_def_12,iPr_def_17),
    introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).

tcf(c_59643,definition,
    iPr_def_19 = hAPP_i1948725293t_bool(ord_less_int,one_one_int),
    introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).

tcf(c_59644,definition,
    iPr_def_20 = hAPP_int_bool(iPr_def_19,t),
    introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).

tcf(c_59645,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_16431,c_59638,c_59639,c_59640,c_59637,c_59641,c_59636,c_59642,c_59634,c_59635]) ).

tcf(c_59646,plain,
    one_one_int != t,
    inference(demodulation,[status(thm)],[c_6324]) ).

tcf(c_59647,plain,
    ~ hBOOL(iPr_def_20),
    inference(demodulation,[status(thm)],[c_6323,c_59643,c_59644]) ).

tcf(c_76314,plain,
    legendre(number_number_of_int(min),iPr_def_18) = one_one_int,
    inference(light_normalisation,[status(thm)],[c_15920,c_59636,c_59637,c_59638,c_59639,c_59640,c_59641,c_59642]) ).

tcf(c_76315,plain,
    hAPP_int_int(plus_plus_int(t),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(t),iPr_def_16))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(light_normalisation,[status(thm)],[c_15972,c_59636,c_59637,c_59638,c_59639,c_59640]) ).

tcf(c_76316,plain,
    hAPP_int_int(plus_plus_int(t),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),t))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_76315,c_253]) ).

tcf(c_76324,plain,
    hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK9),iPr_def_16))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(light_normalisation,[status(thm)],[c_16377,c_59636,c_59637,c_59638,c_59639,c_59640]) ).

tcf(c_76325,plain,
    hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),sK9))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(demodulation,[status(thm)],[c_76324,c_253]) ).

tcf(c_76331,plain,
    ( is_int(iPr_def_14)
    | ~ is_int(one_one_int) ),
    inference(superposition,[status(thm)],[c_59638,c_65]) ).

tcf(c_76332,plain,
    ( is_int(iPr_def_15)
    | ~ is_int(iPr_def_14) ),
    inference(superposition,[status(thm)],[c_59639,c_65]) ).

tcf(c_76333,plain,
    ( is_int(iPr_def_16)
    | ~ is_int(iPr_def_15) ),
    inference(superposition,[status(thm)],[c_59640,c_65]) ).

tcf(c_76334,plain,
    ( is_int(iPr_def_17)
    | ~ is_int(iPr_def_16) ),
    inference(superposition,[status(thm)],[c_59641,c_65]) ).

tcf(c_76335,plain,
    ( is_int(iPr_def_18)
    | ~ is_int(iPr_def_17) ),
    inference(superposition,[status(thm)],[c_59642,c_65]) ).

tcf(c_76336,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),t))) ),
    inference(superposition,[status(thm)],[c_76316,c_65]) ).

tcf(c_76337,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),sK9))) ),
    inference(superposition,[status(thm)],[c_76325,c_65]) ).

tcf(c_76346,plain,
    is_int(iPr_def_14),
    inference(forward_subsumption_resolution,[status(thm)],[c_76331,c_49]) ).

tcf(c_76347,plain,
    is_int(iPr_def_15),
    inference(backward_subsumption_resolution,[status(thm)],[c_76332,c_76346]) ).

tcf(c_76348,plain,
    is_int(iPr_def_16),
    inference(backward_subsumption_resolution,[status(thm)],[c_76333,c_76347]) ).

tcf(c_76349,plain,
    is_int(iPr_def_17),
    inference(backward_subsumption_resolution,[status(thm)],[c_76334,c_76348]) ).

tcf(c_76350,plain,
    is_int(iPr_def_18),
    inference(backward_subsumption_resolution,[status(thm)],[c_76335,c_76349]) ).

tcf(c_76353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_59645]) ).

tcf(c_76354,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_59645]) ).

tcf(c_76355,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_76353,c_59636]) ).

tcf(c_76359,plain,
    hAPP_int_int(iPr_def_12,one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_76355]) ).

tcf(c_76360,plain,
    iPr_def_14 != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_76359,c_59638]) ).

tcf(c_76363,plain,
    hAPP_int_int(iPr_def_13,pls) = pls,
    inference(superposition,[status(thm)],[c_59637,c_1001]) ).

tcf(c_76367,plain,
    hAPP_nat_nat(iPr_def_10,zero_zero_nat) = one_one_nat,
    inference(superposition,[status(thm)],[c_59634,c_1325]) ).

tcf(c_76368,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X0)) != pls,
    inference(light_normalisation,[status(thm)],[c_11299,c_59636]) ).

tcf(c_76369,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int)) != pls,
    inference(superposition,[status(thm)],[c_59636,c_76368]) ).

tcf(c_76370,plain,
    hAPP_int_int(plus_plus_int(one_one_int),iPr_def_14) != pls,
    inference(superposition,[status(thm)],[c_59638,c_76368]) ).

tcf(c_76371,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_15) != pls,
    inference(superposition,[status(thm)],[c_59639,c_76368]) ).

tcf(c_76372,plain,
    hAPP_int_int(plus_plus_int(iPr_def_15),iPr_def_16) != pls,
    inference(superposition,[status(thm)],[c_59640,c_76368]) ).

tcf(c_76373,plain,
    hAPP_int_int(plus_plus_int(iPr_def_17),iPr_def_18) != pls,
    inference(superposition,[status(thm)],[c_59642,c_76368]) ).

tcf(c_76374,plain,
    pls != iPr_def_15,
    inference(light_normalisation,[status(thm)],[c_76370,c_59636,c_59639]) ).

tcf(c_76380,plain,
    ( hBOOL(iPr_def_20)
    | is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_59644,c_1563]) ).

tcf(c_76382,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),
    inference(superposition,[status(thm)],[c_1563,c_756]) ).

tcf(c_76383,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_1563,c_764]) ).

tcf(c_76384,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_1563,c_773]) ).

tcf(c_76385,plain,
    is_int(sK30(iPr_def_19)),
    inference(forward_subsumption_resolution,[status(thm)],[c_76380,c_59647]) ).

tcf(c_76388,plain,
    hBOOL(hAPP_int_bool(zprime,iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_13174,c_59636,c_59638]) ).

tcf(c_76393,plain,
    number_number_of_int(one_one_int) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_254]) ).

tcf(c_76395,plain,
    number_number_of_int(undefined_int(int)) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_254]) ).

tcf(c_76396,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(zfact(X0)) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_254]) ).

tcf(c_76397,plain,
    number_number_of_int(min) = min,
    inference(superposition,[status(thm)],[c_56,c_254]) ).

tcf(c_76398,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(number_number_of_int(X0)) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_254]) ).

tcf(c_76399,plain,
    ! [X0: $i] : number_number_of_int(twoSqu1241645765sum2sq(X0)) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_254]) ).

tcf(c_76400,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(hAPP_int_int(X1,X0)) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_254]) ).

tcf(c_76401,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_nat_int(X0,X1)) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_254]) ).

tcf(c_76402,plain,
    number_number_of_int(m) = m,
    inference(superposition,[status(thm)],[c_70,c_254]) ).

tcf(c_76403,plain,
    number_number_of_int(s1) = s1,
    inference(superposition,[status(thm)],[c_71,c_254]) ).

tcf(c_76404,plain,
    number_number_of_int(s) = s,
    inference(superposition,[status(thm)],[c_72,c_254]) ).

tcf(c_76405,plain,
    number_number_of_int(t) = t,
    inference(superposition,[status(thm)],[c_73,c_254]) ).

tcf(c_76406,plain,
    number_number_of_int(sK9) = sK9,
    inference(superposition,[status(thm)],[c_113,c_254]) ).

tcf(c_76407,plain,
    number_number_of_int(sK10) = sK10,
    inference(superposition,[status(thm)],[c_451,c_254]) ).

tcf(c_76408,plain,
    number_number_of_int(sK11) = sK11,
    inference(superposition,[status(thm)],[c_459,c_254]) ).

tcf(c_76409,plain,
    number_number_of_int(sK13) = sK13,
    inference(superposition,[status(thm)],[c_735,c_254]) ).

tcf(c_76410,plain,
    number_number_of_int(iPr_def_14) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_254]) ).

tcf(c_76411,plain,
    number_number_of_int(iPr_def_15) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_254]) ).

tcf(c_76412,plain,
    number_number_of_int(iPr_def_16) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_254]) ).

tcf(c_76413,plain,
    number_number_of_int(iPr_def_17) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_254]) ).

tcf(c_76414,plain,
    number_number_of_int(iPr_def_18) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_254]) ).

tcf(c_76415,plain,
    number_number_of_int(sK30(iPr_def_19)) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_254]) ).

tcf(c_76416,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_254]) ).

tcf(c_76417,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_254]) ).

tcf(c_76418,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_254]) ).

tcf(c_76426,plain,
    legendre(min,iPr_def_18) = one_one_int,
    inference(demodulation,[status(thm)],[c_76314,c_76397]) ).

tcf(c_76435,plain,
    hAPP_int_int(iPr_def_12,one_one_int) != min,
    inference(superposition,[status(thm)],[c_59636,c_755]) ).

tcf(c_76436,plain,
    min != iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_76435,c_59638]) ).

tcf(c_76437,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(X0),min) = pls,
    inference(light_normalisation,[status(thm)],[c_1633,c_76397]) ).

tcf(c_76443,plain,
    hBOOL(member_int(t,hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),
    inference(superposition,[status(thm)],[c_74,c_226]) ).

tcf(c_76444,plain,
    ! [X0: $i] : hBOOL(member_int(X0,hAPP_i1948725293t_bool(ord_less_eq_int,X0))),
    inference(superposition,[status(thm)],[c_114,c_226]) ).

tcf(c_76445,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(X1))
      | hBOOL(member_int(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_226]) ).

tcf(c_76446,plain,
    hBOOL(member_int(s,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_448,c_226]) ).

tcf(c_76447,plain,
    hBOOL(member_int(sK10,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_452,c_226]) ).

tcf(c_76448,plain,
    hBOOL(member_int(sK11,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_456,c_226]) ).

tcf(c_76449,plain,
    hBOOL(member_int(one_one_int,hAPP_i1948725293t_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_575,c_226]) ).

tcf(c_76450,plain,
    hBOOL(member_int(pls,hAPP_i1948725293t_bool(ord_less_int,min))),
    inference(superposition,[status(thm)],[c_768,c_226]) ).

tcf(c_76451,plain,
    hBOOL(member_int(pls,hAPP_i1948725293t_bool(ord_less_eq_int,min))),
    inference(superposition,[status(thm)],[c_774,c_226]) ).

tcf(c_76452,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(X1,X1))),
    inference(superposition,[status(thm)],[c_815,c_226]) ).

tcf(c_76453,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(one_one_int,zcong(X0,X1))),
    inference(superposition,[status(thm)],[c_829,c_226]) ).

tcf(c_76454,plain,
    hBOOL(member_int(one_one_int,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_846,c_226]) ).

tcf(c_76455,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(X0,pls))),
    inference(superposition,[status(thm)],[c_913,c_226]) ).

tcf(c_76456,plain,
    ! [X0: $i] : hBOOL(member_int(pls,hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_954,c_226]) ).

tcf(c_76457,plain,
    ! [X0: $i] : hBOOL(member_int(X0,hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_961,c_226]) ).

tcf(c_76458,plain,
    ! [X0: $i] : hBOOL(member_int(X0,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_1051,c_226]) ).

tcf(c_76459,plain,
    hBOOL(member_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),twoSqu1154269391sum2sq)),
    inference(superposition,[status(thm)],[c_15973,c_226]) ).

tcf(c_76460,plain,
    hBOOL(member_int(iPr_def_14,zprime)),
    inference(superposition,[status(thm)],[c_76388,c_226]) ).

tcf(c_76489,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),zero_zero_real)),
    inference(superposition,[status(thm)],[c_999,c_1040]) ).

tcf(c_76493,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),zero_zero_nat)),
    inference(superposition,[status(thm)],[c_1337,c_1041]) ).

tcf(c_76495,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),pls)),
    inference(superposition,[status(thm)],[c_1001,c_1042]) ).

tcf(c_76496,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),one_one_int)),
    inference(superposition,[status(thm)],[c_2495,c_1042]) ).

tcf(c_76497,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_59637,c_1042]) ).

tcf(c_76498,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),X1),hAPP_i1948725293t_bool(dvd_dvd_int,X1))),
    inference(superposition,[status(thm)],[c_1042,c_226]) ).

tcf(c_76515,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X0)) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(light_normalisation,[status(thm)],[c_11651,c_59636]) ).

tcf(c_76516,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int)) != hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_59636,c_76515]) ).

tcf(c_76517,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(one_one_int),iPr_def_14),
    inference(superposition,[status(thm)],[c_59638,c_76515]) ).

tcf(c_76518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_15),
    inference(superposition,[status(thm)],[c_59639,c_76515]) ).

tcf(c_76519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(iPr_def_15),iPr_def_16),
    inference(superposition,[status(thm)],[c_59640,c_76515]) ).

tcf(c_76520,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(iPr_def_17),iPr_def_18),
    inference(superposition,[status(thm)],[c_59642,c_76515]) ).

tcf(c_76521,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != iPr_def_15,
    inference(light_normalisation,[status(thm)],[c_76517,c_59636,c_59639]) ).

tcf(c_76534,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_59637,c_1045]) ).

tcf(c_76535,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),X1),hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_1045,c_226]) ).

tcf(c_76537,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
    inference(superposition,[status(thm)],[c_325,c_1134]) ).

tcf(c_76539,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),zero_zero_real)),
    inference(superposition,[status(thm)],[c_1002,c_1134]) ).

tcf(c_76541,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
    inference(superposition,[status(thm)],[c_1004,c_1135]) ).

tcf(c_76544,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_13,m))),
    inference(superposition,[status(thm)],[c_59637,c_1135]) ).

tcf(c_76545,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),X0),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_1135,c_226]) ).

tcf(c_76565,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0),
    inference(superposition,[status(thm)],[c_1244,c_11972]) ).

tcf(c_76566,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1245,c_11972]) ).

tcf(c_76567,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X0)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1246,c_11972]) ).

tcf(c_76568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(X3),X1)),
    inference(superposition,[status(thm)],[c_11972,c_11972]) ).

tcf(c_76569,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_11972,c_1245]) ).

tcf(c_76570,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X1)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_11972,c_1246]) ).

tcf(c_76571,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_76565,c_1244]) ).

tcf(c_76577,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(minus_minus_nat(X0),X2))),
    inference(superposition,[status(thm)],[c_11972,c_1299]) ).

tcf(c_76578,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat)),
    inference(superposition,[status(thm)],[c_1244,c_1299]) ).

tcf(c_76584,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(iPr_def_10,X0))),
    inference(superposition,[status(thm)],[c_59634,c_1373]) ).

tcf(c_76588,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(iPr_def_10,X0))),
    inference(superposition,[status(thm)],[c_59634,c_1375]) ).

tcf(c_76590,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),one_one_nat)),
    inference(superposition,[status(thm)],[c_1413,c_1409]) ).

tcf(c_76595,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_16),iPr_def_17)),
    inference(superposition,[status(thm)],[c_59641,c_76497]) ).

tcf(c_76597,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,X0),hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_76497,c_226]) ).

tcf(c_76599,plain,
    hBOOL(member_int(iPr_def_17,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_16))),
    inference(superposition,[status(thm)],[c_76595,c_226]) ).

tcf(c_76602,plain,
    hAPP_int_int(iPr_def_12,one_one_int) != iPr_def_15,
    inference(superposition,[status(thm)],[c_59636,c_76521]) ).

tcf(c_76603,plain,
    iPr_def_14 != iPr_def_15,
    inference(light_normalisation,[status(thm)],[c_76602,c_59638]) ).

tcf(c_76604,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_59641,c_76534]) ).

tcf(c_76605,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),pls)),
    inference(superposition,[status(thm)],[c_76363,c_76534]) ).

tcf(c_76606,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,X0),hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_76534,c_226]) ).

tcf(c_76608,plain,
    hBOOL(member_int(iPr_def_17,hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_76604,c_226]) ).

tcf(c_76610,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(min),min)) = min,
    inference(light_normalisation,[status(thm)],[c_12227,c_59636]) ).

tcf(c_76612,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(min),min)),min) != hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_76610,c_76515]) ).

tcf(c_76613,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(min),min)),min) != pls,
    inference(superposition,[status(thm)],[c_76610,c_76368]) ).

tcf(c_76619,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( number_number_of_int(sK38(X0,X1,X2)) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_254]) ).

tcf(c_76627,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( number_number_of_int(sK39(X0,X1,X2)) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_254]) ).

tcf(c_76647,plain,
    hBOOL(member_int(hAPP_int_int(iPr_def_13,m),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_76544,c_226]) ).

tcf(c_76648,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),iPr_def_11)),
    inference(superposition,[status(thm)],[c_59635,c_76584]) ).

tcf(c_76649,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
    inference(superposition,[status(thm)],[c_76367,c_76584]) ).

tcf(c_76653,plain,
    hBOOL(member_int(pls,hAPP_i1948725293t_bool(dvd_dvd_int,pls))),
    inference(superposition,[status(thm)],[c_76363,c_76597]) ).

tcf(c_76656,plain,
    hBOOL(member_int(pls,hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_76363,c_76606]) ).

tcf(c_76660,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,pls),X0)),
    inference(superposition,[status(thm)],[c_1630,c_1699]) ).

tcf(c_76661,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(X0,pls),min)),
    inference(superposition,[status(thm)],[c_76437,c_1699]) ).

tcf(c_76662,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(X1,hAPP_int_int(div_mod_int(X1),X0)))),
    inference(superposition,[status(thm)],[c_1699,c_226]) ).

tcf(c_76665,plain,
    ! [X0: $i] : hBOOL(member_int(min,zcong(X0,pls))),
    inference(superposition,[status(thm)],[c_76661,c_226]) ).

tcf(c_76700,plain,
    hAPP_int_int(plus_plus_int(pls),number_number_of_int(pls)) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_340,c_12229]) ).

tcf(c_76701,plain,
    hAPP_int_int(plus_plus_int(pls),number_number_of_int(hAPP_int_int(iPr_def_12,one_one_int))) = number_number_of_int(hAPP_int_int(iPr_def_12,one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_12229]) ).

tcf(c_76704,plain,
    hAPP_int_int(plus_plus_int(pls),iPr_def_14) = iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_76701,c_59638,c_76410]) ).

tcf(c_76717,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_13393,c_59636,c_59638]) ).

tcf(c_76718,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_76717,c_226]) ).

tcf(c_76727,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),pls) = iPr_def_14,
    inference(demodulation,[status(thm)],[c_76704,c_257]) ).

tcf(c_76735,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),iPr_def_11)),
    inference(light_normalisation,[status(thm)],[c_13930,c_59634,c_59635]) ).

tcf(c_76737,plain,
    number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_12527]) ).

tcf(c_76744,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(multInv(X0,X1)) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_254]) ).

tcf(c_76756,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(legendre(X0,X1)) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_254]) ).

tcf(c_76767,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(inv(X0,X1)) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_254]) ).

tcf(c_76776,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_118]) ).

tcf(c_76777,plain,
    ( ~ is_int(one_one_int)
    | ~ hBOOL(hAPP_int_bool(iPr_def_19,one_one_int)) ),
    inference(superposition,[status(thm)],[c_59643,c_118]) ).

tcf(c_76778,plain,
    ~ hBOOL(hAPP_int_bool(iPr_def_19,one_one_int)),
    inference(forward_subsumption_resolution,[status(thm)],[c_76777,c_49]) ).

tcf(c_76788,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_254]) ).

tcf(c_76796,plain,
    hBOOL(member_int(one_one_int,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_2495,c_76498]) ).

tcf(c_76804,plain,
    hBOOL(member_int(pls,hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_1004,c_76545]) ).

tcf(c_76810,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(pls,pls))),
    inference(superposition,[status(thm)],[c_1630,c_76662]) ).

tcf(c_76833,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = hAPP_int_int(iPr_def_12,number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_12528,c_59636]) ).

tcf(c_76834,plain,
    number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = hAPP_int_int(iPr_def_12,number_number_of_int(one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_76833]) ).

tcf(c_76835,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_12,number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) ),
    inference(superposition,[status(thm)],[c_76833,c_58]) ).

tcf(c_76836,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))))) = hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))),
    inference(superposition,[status(thm)],[c_76833,c_12229]) ).

tcf(c_76837,plain,
    number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int)))) = iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_76834,c_59638,c_76393]) ).

tcf(c_76855,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),m) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_59637,c_253]) ).

tcf(c_76863,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(X0),X1))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_253,c_65]) ).

tcf(c_76874,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),one_one_int) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_59636,c_257]) ).

tcf(c_76880,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X0),X1))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_257,c_65]) ).

tcf(c_76881,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) = hAPP_int_int(iPr_def_12,number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_257,c_76833]) ).

tcf(c_76882,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))),X0)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(superposition,[status(thm)],[c_257,c_12527]) ).

tcf(c_76886,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,pls)))) = hAPP_int_int(iPr_def_12,number_number_of_int(X0)),
    inference(demodulation,[status(thm)],[c_76833,c_76874]) ).

tcf(c_76887,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,pls)))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(demodulation,[status(thm)],[c_12527,c_76874]) ).

tcf(c_76888,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,pls))) = one_one_nat,
    inference(demodulation,[status(thm)],[c_11300,c_76874]) ).

tcf(c_76889,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,pls))) = one_one_int,
    inference(demodulation,[status(thm)],[c_11296,c_76874]) ).

tcf(c_76890,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,pls))) = one_one_real,
    inference(demodulation,[status(thm)],[c_11295,c_76874]) ).

tcf(c_76901,plain,
    hAPP_int_int(times_times_int(pls),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_57,c_346]) ).

tcf(c_76902,plain,
    hAPP_int_int(times_times_int(undefined_int(int)),one_one_int) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_346]) ).

tcf(c_76903,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(multInv(X0,X1)),one_one_int) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_346]) ).

tcf(c_76904,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(zfact(X0)),one_one_int) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_346]) ).

tcf(c_76905,plain,
    hAPP_int_int(times_times_int(min),one_one_int) = min,
    inference(superposition,[status(thm)],[c_56,c_346]) ).

tcf(c_76906,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_346]) ).

tcf(c_76907,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(legendre(X0,X1)),one_one_int) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_346]) ).

tcf(c_76908,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),one_one_int) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_346]) ).

tcf(c_76909,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(inv(X0,X1)),one_one_int) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_346]) ).

tcf(c_76910,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(X1,X0)),one_one_int) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_346]) ).

tcf(c_76911,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),one_one_int) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_346]) ).

tcf(c_76912,plain,
    hAPP_int_int(times_times_int(m),one_one_int) = m,
    inference(superposition,[status(thm)],[c_70,c_346]) ).

tcf(c_76913,plain,
    hAPP_int_int(times_times_int(s1),one_one_int) = s1,
    inference(superposition,[status(thm)],[c_71,c_346]) ).

tcf(c_76914,plain,
    hAPP_int_int(times_times_int(s),one_one_int) = s,
    inference(superposition,[status(thm)],[c_72,c_346]) ).

tcf(c_76915,plain,
    hAPP_int_int(times_times_int(t),one_one_int) = t,
    inference(superposition,[status(thm)],[c_73,c_346]) ).

tcf(c_76916,plain,
    hAPP_int_int(times_times_int(sK9),one_one_int) = sK9,
    inference(superposition,[status(thm)],[c_113,c_346]) ).

tcf(c_76917,plain,
    hAPP_int_int(times_times_int(sK10),one_one_int) = sK10,
    inference(superposition,[status(thm)],[c_451,c_346]) ).

tcf(c_76918,plain,
    hAPP_int_int(times_times_int(sK11),one_one_int) = sK11,
    inference(superposition,[status(thm)],[c_459,c_346]) ).

tcf(c_76919,plain,
    hAPP_int_int(times_times_int(sK13),one_one_int) = sK13,
    inference(superposition,[status(thm)],[c_735,c_346]) ).

tcf(c_76920,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(sK38(X0,X1,X2)),one_one_int) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_346]) ).

tcf(c_76921,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(sK39(X0,X1,X2)),one_one_int) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_346]) ).

tcf(c_76924,plain,
    hAPP_int_int(times_times_int(iPr_def_14),one_one_int) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_346]) ).

tcf(c_76925,plain,
    hAPP_int_int(times_times_int(iPr_def_15),one_one_int) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_346]) ).

tcf(c_76926,plain,
    hAPP_int_int(times_times_int(iPr_def_16),one_one_int) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_346]) ).

tcf(c_76927,plain,
    hAPP_int_int(times_times_int(iPr_def_17),one_one_int) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_346]) ).

tcf(c_76928,plain,
    hAPP_int_int(times_times_int(iPr_def_18),one_one_int) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_346]) ).

tcf(c_76929,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_346]) ).

tcf(c_76930,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_346]) ).

tcf(c_76931,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_346]) ).

tcf(c_76932,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_346]) ).

tcf(c_76933,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_346]) ).

tcf(c_76934,plain,
    hAPP_int_int(iPr_def_13,one_one_int) = m,
    inference(light_normalisation,[status(thm)],[c_76912,c_59637]) ).

tcf(c_76973,plain,
    hBOOL(member_int(m,hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_76934,c_76606]) ).

tcf(c_76974,plain,
    hBOOL(member_int(m,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76934,c_76597]) ).

tcf(c_76975,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),m)),
    inference(superposition,[status(thm)],[c_76934,c_76534]) ).

tcf(c_76976,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),m)),
    inference(superposition,[status(thm)],[c_76934,c_76497]) ).

tcf(c_76977,plain,
    hAPP_int_int(times_times_int(one_one_int),min) = min,
    inference(demodulation,[status(thm)],[c_76905,c_253]) ).

tcf(c_76979,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),min)),
    inference(superposition,[status(thm)],[c_76977,c_1042]) ).

tcf(c_76980,plain,
    hBOOL(member_int(min,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76977,c_76535]) ).

tcf(c_76981,plain,
    hBOOL(member_int(min,hAPP_i1948725293t_bool(dvd_dvd_int,min))),
    inference(superposition,[status(thm)],[c_76977,c_76498]) ).

tcf(c_76982,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),min)),
    inference(superposition,[status(thm)],[c_76977,c_1045]) ).

tcf(c_76983,plain,
    hAPP_int_int(times_times_int(one_one_int),s1) = s1,
    inference(demodulation,[status(thm)],[c_76913,c_253]) ).

tcf(c_76985,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,s1),s1)),
    inference(superposition,[status(thm)],[c_76983,c_1042]) ).

tcf(c_76986,plain,
    hBOOL(member_int(s1,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76983,c_76535]) ).

tcf(c_76987,plain,
    hBOOL(member_int(s1,hAPP_i1948725293t_bool(dvd_dvd_int,s1))),
    inference(superposition,[status(thm)],[c_76983,c_76498]) ).

tcf(c_76988,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),s1)),
    inference(superposition,[status(thm)],[c_76983,c_1045]) ).

tcf(c_76989,plain,
    hAPP_int_int(times_times_int(one_one_int),s) = s,
    inference(demodulation,[status(thm)],[c_76914,c_253]) ).

tcf(c_76991,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,s),s)),
    inference(superposition,[status(thm)],[c_76989,c_1042]) ).

tcf(c_76992,plain,
    hBOOL(member_int(s,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76989,c_76535]) ).

tcf(c_76993,plain,
    hBOOL(member_int(s,hAPP_i1948725293t_bool(dvd_dvd_int,s))),
    inference(superposition,[status(thm)],[c_76989,c_76498]) ).

tcf(c_76994,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),s)),
    inference(superposition,[status(thm)],[c_76989,c_1045]) ).

tcf(c_76995,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)) = sK30(iPr_def_19),
    inference(demodulation,[status(thm)],[c_76929,c_253]) ).

tcf(c_76997,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_1042]) ).

tcf(c_76998,plain,
    hBOOL(member_int(sK30(iPr_def_19),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76995,c_76535]) ).

tcf(c_76999,plain,
    hBOOL(member_int(sK30(iPr_def_19),hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76995,c_76498]) ).

tcf(c_77000,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_1045]) ).

tcf(c_77001,plain,
    hAPP_int_int(times_times_int(one_one_int),t) = t,
    inference(demodulation,[status(thm)],[c_76915,c_253]) ).

tcf(c_77003,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,t),t)),
    inference(superposition,[status(thm)],[c_77001,c_1042]) ).

tcf(c_77004,plain,
    hBOOL(member_int(t,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77001,c_76535]) ).

tcf(c_77005,plain,
    hBOOL(member_int(t,hAPP_i1948725293t_bool(dvd_dvd_int,t))),
    inference(superposition,[status(thm)],[c_77001,c_76498]) ).

tcf(c_77006,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),t)),
    inference(superposition,[status(thm)],[c_77001,c_1045]) ).

tcf(c_77007,plain,
    hAPP_int_int(times_times_int(one_one_int),sK9) = sK9,
    inference(demodulation,[status(thm)],[c_76916,c_253]) ).

tcf(c_77009,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK9),sK9)),
    inference(superposition,[status(thm)],[c_77007,c_1042]) ).

tcf(c_77010,plain,
    hBOOL(member_int(sK9,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77007,c_76535]) ).

tcf(c_77011,plain,
    hBOOL(member_int(sK9,hAPP_i1948725293t_bool(dvd_dvd_int,sK9))),
    inference(superposition,[status(thm)],[c_77007,c_76498]) ).

tcf(c_77012,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK9)),
    inference(superposition,[status(thm)],[c_77007,c_1045]) ).

tcf(c_77013,plain,
    hAPP_int_int(times_times_int(one_one_int),sK10) = sK10,
    inference(demodulation,[status(thm)],[c_76917,c_253]) ).

tcf(c_77015,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK10),sK10)),
    inference(superposition,[status(thm)],[c_77013,c_1042]) ).

tcf(c_77016,plain,
    hBOOL(member_int(sK10,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77013,c_76535]) ).

tcf(c_77017,plain,
    hBOOL(member_int(sK10,hAPP_i1948725293t_bool(dvd_dvd_int,sK10))),
    inference(superposition,[status(thm)],[c_77013,c_76498]) ).

tcf(c_77018,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK10)),
    inference(superposition,[status(thm)],[c_77013,c_1045]) ).

tcf(c_77019,plain,
    hAPP_int_int(times_times_int(one_one_int),sK11) = sK11,
    inference(demodulation,[status(thm)],[c_76918,c_253]) ).

tcf(c_77021,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK11),sK11)),
    inference(superposition,[status(thm)],[c_77019,c_1042]) ).

tcf(c_77022,plain,
    hBOOL(member_int(sK11,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77019,c_76535]) ).

tcf(c_77023,plain,
    hBOOL(member_int(sK11,hAPP_i1948725293t_bool(dvd_dvd_int,sK11))),
    inference(superposition,[status(thm)],[c_77019,c_76498]) ).

tcf(c_77024,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK11)),
    inference(superposition,[status(thm)],[c_77019,c_1045]) ).

tcf(c_77025,plain,
    hAPP_int_int(times_times_int(one_one_int),sK13) = sK13,
    inference(demodulation,[status(thm)],[c_76919,c_253]) ).

tcf(c_77027,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK13),sK13)),
    inference(superposition,[status(thm)],[c_77025,c_1042]) ).

tcf(c_77028,plain,
    hBOOL(member_int(sK13,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77025,c_76535]) ).

tcf(c_77029,plain,
    hBOOL(member_int(sK13,hAPP_i1948725293t_bool(dvd_dvd_int,sK13))),
    inference(superposition,[status(thm)],[c_77025,c_76498]) ).

tcf(c_77030,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK13)),
    inference(superposition,[status(thm)],[c_77025,c_1045]) ).

tcf(c_77032,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76924,c_1042]) ).

tcf(c_77033,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14))),
    inference(superposition,[status(thm)],[c_76924,c_76535]) ).

tcf(c_77034,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76924,c_76498]) ).

tcf(c_77035,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76924,c_1045]) ).

tcf(c_77037,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76925,c_1042]) ).

tcf(c_77038,plain,
    hBOOL(member_int(iPr_def_15,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_15))),
    inference(superposition,[status(thm)],[c_76925,c_76535]) ).

tcf(c_77039,plain,
    hBOOL(member_int(iPr_def_15,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76925,c_76498]) ).

tcf(c_77040,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_15),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76925,c_1045]) ).

tcf(c_77044,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,X0))
      | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_76855,c_65]) ).

tcf(c_77049,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(m),X0) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_76855,c_253]) ).

tcf(c_77054,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_77044,c_70]) ).

tcf(c_77062,plain,
    hAPP_int_int(times_times_int(one_one_int),pls) = pls,
    inference(superposition,[status(thm)],[c_57,c_347]) ).

tcf(c_77063,plain,
    hAPP_int_int(times_times_int(one_one_int),undefined_int(int)) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_347]) ).

tcf(c_77064,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),multInv(X0,X1)) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_347]) ).

tcf(c_77065,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),zfact(X0)) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_347]) ).

tcf(c_77067,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_347]) ).

tcf(c_77068,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),legendre(X0,X1)) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_347]) ).

tcf(c_77069,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),twoSqu1241645765sum2sq(X0)) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_347]) ).

tcf(c_77070,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),inv(X0,X1)) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_347]) ).

tcf(c_77071,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(X1,X0)) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_347]) ).

tcf(c_77072,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_nat_int(X0,X1)) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_347]) ).

tcf(c_77073,plain,
    hAPP_int_int(times_times_int(one_one_int),m) = m,
    inference(superposition,[status(thm)],[c_70,c_347]) ).

tcf(c_77081,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(one_one_int),sK38(X0,X1,X2)) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_347]) ).

tcf(c_77082,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(one_one_int),sK39(X0,X1,X2)) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_347]) ).

tcf(c_77085,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_14) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_347]) ).

tcf(c_77086,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_15) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_347]) ).

tcf(c_77087,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_16) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_347]) ).

tcf(c_77088,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_17) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_347]) ).

tcf(c_77089,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_18) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_347]) ).

tcf(c_77091,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_347]) ).

tcf(c_77092,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,min))) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_347]) ).

tcf(c_77093,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_347]) ).

tcf(c_77094,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_347]) ).

tcf(c_77136,plain,
    hAPP_int_int(plus_plus_int(pls),one_one_int) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_523]) ).

tcf(c_77138,plain,
    hAPP_int_int(plus_plus_int(pls),undefined_int(int)) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_523]) ).

tcf(c_77139,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),multInv(X0,X1)) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_523]) ).

tcf(c_77140,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),zfact(X0)) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_523]) ).

tcf(c_77141,plain,
    hAPP_int_int(plus_plus_int(pls),min) = min,
    inference(superposition,[status(thm)],[c_56,c_523]) ).

tcf(c_77142,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),number_number_of_int(X0)) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_523]) ).

tcf(c_77143,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),legendre(X0,X1)) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_523]) ).

tcf(c_77144,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),twoSqu1241645765sum2sq(X0)) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_523]) ).

tcf(c_77145,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),inv(X0,X1)) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_523]) ).

tcf(c_77146,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(X1,X0)) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_523]) ).

tcf(c_77147,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(X0,X1)) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_523]) ).

tcf(c_77148,plain,
    hAPP_int_int(plus_plus_int(pls),m) = m,
    inference(superposition,[status(thm)],[c_70,c_523]) ).

tcf(c_77149,plain,
    hAPP_int_int(plus_plus_int(pls),s1) = s1,
    inference(superposition,[status(thm)],[c_71,c_523]) ).

tcf(c_77150,plain,
    hAPP_int_int(plus_plus_int(pls),s) = s,
    inference(superposition,[status(thm)],[c_72,c_523]) ).

tcf(c_77151,plain,
    hAPP_int_int(plus_plus_int(pls),t) = t,
    inference(superposition,[status(thm)],[c_73,c_523]) ).

tcf(c_77152,plain,
    hAPP_int_int(plus_plus_int(pls),sK9) = sK9,
    inference(superposition,[status(thm)],[c_113,c_523]) ).

tcf(c_77153,plain,
    hAPP_int_int(plus_plus_int(pls),sK10) = sK10,
    inference(superposition,[status(thm)],[c_451,c_523]) ).

tcf(c_77154,plain,
    hAPP_int_int(plus_plus_int(pls),sK11) = sK11,
    inference(superposition,[status(thm)],[c_459,c_523]) ).

tcf(c_77155,plain,
    hAPP_int_int(plus_plus_int(pls),sK13) = sK13,
    inference(superposition,[status(thm)],[c_735,c_523]) ).

tcf(c_77156,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(pls),sK38(X0,X1,X2)) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_523]) ).

tcf(c_77157,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(pls),sK39(X0,X1,X2)) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_523]) ).

tcf(c_77161,plain,
    hAPP_int_int(plus_plus_int(pls),iPr_def_15) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_523]) ).

tcf(c_77162,plain,
    hAPP_int_int(plus_plus_int(pls),iPr_def_16) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_523]) ).

tcf(c_77163,plain,
    hAPP_int_int(plus_plus_int(pls),iPr_def_17) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_523]) ).

tcf(c_77164,plain,
    hAPP_int_int(plus_plus_int(pls),iPr_def_18) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_523]) ).

tcf(c_77165,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(iPr_def_19)) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_523]) ).

tcf(c_77166,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_523]) ).

tcf(c_77167,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,min))) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_523]) ).

tcf(c_77168,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_523]) ).

tcf(c_77169,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_523]) ).

tcf(c_77211,plain,
    hAPP_int_int(plus_plus_int(one_one_int),pls) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_524]) ).

tcf(c_77213,plain,
    hAPP_int_int(plus_plus_int(undefined_int(int)),pls) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_524]) ).

tcf(c_77214,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(multInv(X0,X1)),pls) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_524]) ).

tcf(c_77215,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(zfact(X0)),pls) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_524]) ).

tcf(c_77216,plain,
    hAPP_int_int(plus_plus_int(min),pls) = min,
    inference(superposition,[status(thm)],[c_56,c_524]) ).

tcf(c_77217,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(X0)),pls) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_524]) ).

tcf(c_77218,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(legendre(X0,X1)),pls) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_524]) ).

tcf(c_77219,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),pls) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_524]) ).

tcf(c_77220,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(inv(X0,X1)),pls) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_524]) ).

tcf(c_77221,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(X1,X0)),pls) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_524]) ).

tcf(c_77222,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(X0,X1)),pls) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_524]) ).

tcf(c_77223,plain,
    hAPP_int_int(plus_plus_int(m),pls) = m,
    inference(superposition,[status(thm)],[c_70,c_524]) ).

tcf(c_77224,plain,
    hAPP_int_int(plus_plus_int(s1),pls) = s1,
    inference(superposition,[status(thm)],[c_71,c_524]) ).

tcf(c_77225,plain,
    hAPP_int_int(plus_plus_int(s),pls) = s,
    inference(superposition,[status(thm)],[c_72,c_524]) ).

tcf(c_77226,plain,
    hAPP_int_int(plus_plus_int(t),pls) = t,
    inference(superposition,[status(thm)],[c_73,c_524]) ).

tcf(c_77227,plain,
    hAPP_int_int(plus_plus_int(sK9),pls) = sK9,
    inference(superposition,[status(thm)],[c_113,c_524]) ).

tcf(c_77228,plain,
    hAPP_int_int(plus_plus_int(sK10),pls) = sK10,
    inference(superposition,[status(thm)],[c_451,c_524]) ).

tcf(c_77229,plain,
    hAPP_int_int(plus_plus_int(sK11),pls) = sK11,
    inference(superposition,[status(thm)],[c_459,c_524]) ).

tcf(c_77230,plain,
    hAPP_int_int(plus_plus_int(sK13),pls) = sK13,
    inference(superposition,[status(thm)],[c_735,c_524]) ).

tcf(c_77231,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK38(X0,X1,X2)),pls) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_524]) ).

tcf(c_77232,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK39(X0,X1,X2)),pls) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_524]) ).

tcf(c_77236,plain,
    hAPP_int_int(plus_plus_int(iPr_def_15),pls) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_524]) ).

tcf(c_77237,plain,
    hAPP_int_int(plus_plus_int(iPr_def_16),pls) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_524]) ).

tcf(c_77238,plain,
    hAPP_int_int(plus_plus_int(iPr_def_17),pls) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_524]) ).

tcf(c_77239,plain,
    hAPP_int_int(plus_plus_int(iPr_def_18),pls) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_524]) ).

tcf(c_77240,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),pls) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_524]) ).

tcf(c_77241,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_524]) ).

tcf(c_77242,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_524]) ).

tcf(c_77243,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_524]) ).

tcf(c_77244,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_524]) ).

tcf(c_77245,plain,
    hAPP_int_int(iPr_def_12,pls) = one_one_int,
    inference(light_normalisation,[status(thm)],[c_77211,c_59636]) ).

tcf(c_77287,plain,
    hAPP_nat_int(power_power_int(one_one_int),one_one_nat) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_608]) ).

tcf(c_77288,plain,
    hAPP_nat_int(power_power_int(pls),one_one_nat) = pls,
    inference(superposition,[status(thm)],[c_57,c_608]) ).

tcf(c_77289,plain,
    hAPP_nat_int(power_power_int(undefined_int(int)),one_one_nat) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_608]) ).

tcf(c_77290,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(multInv(X0,X1)),one_one_nat) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_608]) ).

tcf(c_77291,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(zfact(X0)),one_one_nat) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_608]) ).

tcf(c_77292,plain,
    hAPP_nat_int(power_power_int(min),one_one_nat) = min,
    inference(superposition,[status(thm)],[c_56,c_608]) ).

tcf(c_77293,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(number_number_of_int(X0)),one_one_nat) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_608]) ).

tcf(c_77294,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(legendre(X0,X1)),one_one_nat) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_608]) ).

tcf(c_77295,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(twoSqu1241645765sum2sq(X0)),one_one_nat) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_608]) ).

tcf(c_77296,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(inv(X0,X1)),one_one_nat) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_608]) ).

tcf(c_77297,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(hAPP_int_int(X1,X0)),one_one_nat) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_608]) ).

tcf(c_77298,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(X0,X1)),one_one_nat) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_608]) ).

tcf(c_77299,plain,
    hAPP_nat_int(power_power_int(m),one_one_nat) = m,
    inference(superposition,[status(thm)],[c_70,c_608]) ).

tcf(c_77300,plain,
    hAPP_nat_int(power_power_int(s1),one_one_nat) = s1,
    inference(superposition,[status(thm)],[c_71,c_608]) ).

tcf(c_77301,plain,
    hAPP_nat_int(power_power_int(s),one_one_nat) = s,
    inference(superposition,[status(thm)],[c_72,c_608]) ).

tcf(c_77302,plain,
    hAPP_nat_int(power_power_int(t),one_one_nat) = t,
    inference(superposition,[status(thm)],[c_73,c_608]) ).

tcf(c_77303,plain,
    hAPP_nat_int(power_power_int(sK9),one_one_nat) = sK9,
    inference(superposition,[status(thm)],[c_113,c_608]) ).

tcf(c_77304,plain,
    hAPP_nat_int(power_power_int(sK10),one_one_nat) = sK10,
    inference(superposition,[status(thm)],[c_451,c_608]) ).

tcf(c_77305,plain,
    hAPP_nat_int(power_power_int(sK11),one_one_nat) = sK11,
    inference(superposition,[status(thm)],[c_459,c_608]) ).

tcf(c_77306,plain,
    hAPP_nat_int(power_power_int(sK13),one_one_nat) = sK13,
    inference(superposition,[status(thm)],[c_735,c_608]) ).

tcf(c_77307,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_nat_int(power_power_int(sK38(X0,X1,X2)),one_one_nat) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_608]) ).

tcf(c_77308,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_nat_int(power_power_int(sK39(X0,X1,X2)),one_one_nat) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_608]) ).

tcf(c_77311,plain,
    hAPP_nat_int(power_power_int(iPr_def_14),one_one_nat) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_608]) ).

tcf(c_77312,plain,
    hAPP_nat_int(power_power_int(iPr_def_15),one_one_nat) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_608]) ).

tcf(c_77313,plain,
    hAPP_nat_int(power_power_int(iPr_def_16),one_one_nat) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_608]) ).

tcf(c_77314,plain,
    hAPP_nat_int(power_power_int(iPr_def_17),one_one_nat) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_608]) ).

tcf(c_77315,plain,
    hAPP_nat_int(power_power_int(iPr_def_18),one_one_nat) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_608]) ).

tcf(c_77316,plain,
    hAPP_nat_int(power_power_int(sK30(iPr_def_19)),one_one_nat) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_608]) ).

tcf(c_77317,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_608]) ).

tcf(c_77318,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_608]) ).

tcf(c_77319,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_608]) ).

tcf(c_77320,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_608]) ).

tcf(c_77361,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,X0)),one_one_nat) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_608]) ).

tcf(c_77362,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),pls) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_524]) ).

tcf(c_77363,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_13,X0)) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_523]) ).

tcf(c_77364,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(iPr_def_13,X0)) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_347]) ).

tcf(c_77365,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),one_one_int) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_346]) ).

tcf(c_77366,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(iPr_def_13,X0)) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_254]) ).

tcf(c_77374,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != hAPP_int_int(plus_plus_int(pls),one_one_int),
    inference(superposition,[status(thm)],[c_77245,c_76515]) ).

tcf(c_77375,plain,
    hAPP_int_int(plus_plus_int(pls),one_one_int) != pls,
    inference(superposition,[status(thm)],[c_77245,c_76368]) ).

tcf(c_77377,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) != one_one_int,
    inference(light_normalisation,[status(thm)],[c_77374,c_77136]) ).

tcf(c_77380,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76926,c_1042]) ).

tcf(c_77381,plain,
    hBOOL(member_int(iPr_def_16,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_16))),
    inference(superposition,[status(thm)],[c_76926,c_76535]) ).

tcf(c_77382,plain,
    hBOOL(member_int(iPr_def_16,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76926,c_76498]) ).

tcf(c_77383,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_16),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76926,c_1045]) ).

tcf(c_77385,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76927,c_1042]) ).

tcf(c_77386,plain,
    hBOOL(member_int(iPr_def_17,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_17))),
    inference(superposition,[status(thm)],[c_76927,c_76535]) ).

tcf(c_77387,plain,
    hBOOL(member_int(iPr_def_17,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76927,c_76498]) ).

tcf(c_77388,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_17),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76927,c_1045]) ).

tcf(c_77393,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76928,c_1042]) ).

tcf(c_77394,plain,
    hBOOL(member_int(iPr_def_18,hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_18))),
    inference(superposition,[status(thm)],[c_76928,c_76535]) ).

tcf(c_77395,plain,
    hBOOL(member_int(iPr_def_18,hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_76928,c_76498]) ).

tcf(c_77396,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_18),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76928,c_1045]) ).

tcf(c_77402,plain,
    hAPP_int_int(minus_minus_int(one_one_int),pls) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_880]) ).

tcf(c_77403,plain,
    hAPP_int_int(minus_minus_int(pls),pls) = pls,
    inference(superposition,[status(thm)],[c_57,c_880]) ).

tcf(c_77404,plain,
    hAPP_int_int(minus_minus_int(undefined_int(int)),pls) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_880]) ).

tcf(c_77405,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(multInv(X0,X1)),pls) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_880]) ).

tcf(c_77406,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(zfact(X0)),pls) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_880]) ).

tcf(c_77407,plain,
    hAPP_int_int(minus_minus_int(min),pls) = min,
    inference(superposition,[status(thm)],[c_56,c_880]) ).

tcf(c_77408,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),pls) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_880]) ).

tcf(c_77409,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(legendre(X0,X1)),pls) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_880]) ).

tcf(c_77410,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),pls) = twoSqu1241645765sum2sq(X0),
    inference(superposition,[status(thm)],[c_61,c_880]) ).

tcf(c_77411,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(inv(X0,X1)),pls) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_880]) ).

tcf(c_77412,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(X1,X0)),pls) = hAPP_int_int(X1,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_880]) ).

tcf(c_77413,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),pls) = hAPP_nat_int(X0,X1),
    inference(superposition,[status(thm)],[c_67,c_880]) ).

tcf(c_77414,plain,
    hAPP_int_int(minus_minus_int(m),pls) = m,
    inference(superposition,[status(thm)],[c_70,c_880]) ).

tcf(c_77415,plain,
    hAPP_int_int(minus_minus_int(s1),pls) = s1,
    inference(superposition,[status(thm)],[c_71,c_880]) ).

tcf(c_77416,plain,
    hAPP_int_int(minus_minus_int(s),pls) = s,
    inference(superposition,[status(thm)],[c_72,c_880]) ).

tcf(c_77417,plain,
    hAPP_int_int(minus_minus_int(t),pls) = t,
    inference(superposition,[status(thm)],[c_73,c_880]) ).

tcf(c_77418,plain,
    hAPP_int_int(minus_minus_int(sK9),pls) = sK9,
    inference(superposition,[status(thm)],[c_113,c_880]) ).

tcf(c_77419,plain,
    hAPP_int_int(minus_minus_int(sK10),pls) = sK10,
    inference(superposition,[status(thm)],[c_451,c_880]) ).

tcf(c_77420,plain,
    hAPP_int_int(minus_minus_int(sK11),pls) = sK11,
    inference(superposition,[status(thm)],[c_459,c_880]) ).

tcf(c_77421,plain,
    hAPP_int_int(minus_minus_int(sK13),pls) = sK13,
    inference(superposition,[status(thm)],[c_735,c_880]) ).

tcf(c_77422,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(minus_minus_int(sK38(X0,X1,X2)),pls) = sK38(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1651,c_880]) ).

tcf(c_77423,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | ( hAPP_int_int(minus_minus_int(sK39(X0,X1,X2)),pls) = sK39(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1652,c_880]) ).

tcf(c_77426,plain,
    hAPP_int_int(minus_minus_int(iPr_def_14),pls) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_880]) ).

tcf(c_77427,plain,
    hAPP_int_int(minus_minus_int(iPr_def_15),pls) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_880]) ).

tcf(c_77428,plain,
    hAPP_int_int(minus_minus_int(iPr_def_16),pls) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_880]) ).

tcf(c_77429,plain,
    hAPP_int_int(minus_minus_int(iPr_def_17),pls) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_880]) ).

tcf(c_77430,plain,
    hAPP_int_int(minus_minus_int(iPr_def_18),pls) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_880]) ).

tcf(c_77431,plain,
    hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),pls) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_880]) ).

tcf(c_77432,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_880]) ).

tcf(c_77433,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_880]) ).

tcf(c_77434,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_880]) ).

tcf(c_77435,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_880]) ).

tcf(c_77436,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),pls) = hAPP_int_int(iPr_def_13,X0),
    inference(superposition,[status(thm)],[c_77054,c_880]) ).

tcf(c_77479,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | is_int(sK15(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_945]) ).

tcf(c_77503,plain,
    ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
    inference(superposition,[status(thm)],[c_325,c_1201]) ).

tcf(c_77505,plain,
    ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),zero_zero_real)),
    inference(superposition,[status(thm)],[c_1002,c_1201]) ).

tcf(c_77521,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),one_one_nat) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_59634,c_1284]) ).

tcf(c_77538,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),X0) = one_one_nat,
    inference(superposition,[status(thm)],[c_59634,c_1289]) ).

tcf(c_77549,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),one_one_nat) = X0,
    inference(superposition,[status(thm)],[c_59634,c_1290]) ).

tcf(c_77552,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X0)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
    inference(superposition,[status(thm)],[c_1290,c_11972]) ).

tcf(c_77592,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1284,c_1327]) ).

tcf(c_77596,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(iPr_def_10,X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_59634,c_1327]) ).

tcf(c_77599,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1327,c_11972]) ).

tcf(c_77600,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),X1)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1327,c_11972]) ).

tcf(c_77608,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,X0)),one_one_nat)),
    inference(superposition,[status(thm)],[c_59634,c_1343]) ).

tcf(c_77614,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,X0)),X0)),
    inference(superposition,[status(thm)],[c_59634,c_1344]) ).

tcf(c_77637,plain,
    ! [X0: $i] :
      ( is_int(sK26(X0))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_1509,c_59643]) ).

tcf(c_77667,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1309,c_1684]) ).

tcf(c_77669,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(X0),X0) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1413,c_1684]) ).

tcf(c_77670,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(X0),one_one_nat) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1417,c_1684]) ).

tcf(c_77672,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(zero_zero_nat),X0) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1337,c_1684]) ).

tcf(c_77673,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))),
    inference(superposition,[status(thm)],[c_1684,c_1694]) ).

tcf(c_77694,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0)))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(light_normalisation,[status(thm)],[c_12529,c_59636]) ).

tcf(c_77695,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_14))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(one_one_int)),
    inference(superposition,[status(thm)],[c_59638,c_77694]) ).

tcf(c_77696,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_15))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(iPr_def_14)),
    inference(superposition,[status(thm)],[c_59639,c_77694]) ).

tcf(c_77697,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_16))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(iPr_def_15)),
    inference(superposition,[status(thm)],[c_59640,c_77694]) ).

tcf(c_77698,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_18))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(iPr_def_17)),
    inference(superposition,[status(thm)],[c_59642,c_77694]) ).

tcf(c_77699,plain,
    hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(plus_plus_int(min),min))) = number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),min))),
    inference(superposition,[status(thm)],[c_76610,c_77694]) ).

tcf(c_77700,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(pls)),
    inference(superposition,[status(thm)],[c_77245,c_77694]) ).

tcf(c_77701,plain,
    number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = hAPP_real_real(plus_plus_real(one_one_real),zero_zero_real),
    inference(light_normalisation,[status(thm)],[c_77700,c_568]) ).

tcf(c_77702,plain,
    hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(plus_plus_int(min),min))) = number267125858f_real(min),
    inference(light_normalisation,[status(thm)],[c_77699,c_77141]) ).

tcf(c_77703,plain,
    is_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_1563,c_11305]) ).

tcf(c_77704,plain,
    ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),pls)),
    inference(superposition,[status(thm)],[c_1004,c_11305]) ).

tcf(c_77706,plain,
    ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),one_one_int)),
    inference(superposition,[status(thm)],[c_2495,c_11305]) ).

tcf(c_77707,plain,
    ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_13,m))),
    inference(superposition,[status(thm)],[c_76855,c_11305]) ).

tcf(c_77713,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(member_int(X0,hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) ),
    inference(superposition,[status(thm)],[c_46418,c_226]) ).

tcf(c_77714,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X2))
      | sP3(X0,sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),X1) ),
    inference(superposition,[status(thm)],[c_46418,c_1561]) ).

tcf(c_77729,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(iPr_def_12,pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_76355]) ).

tcf(c_77730,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_59645]) ).

tcf(c_77731,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_59645]) ).

tcf(c_77732,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( one_one_int != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_77729,c_77245]) ).

tcf(c_77747,plain,
    hAPP_int_int(minus_minus_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),pls) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_880]) ).

tcf(c_77748,plain,
    hAPP_nat_int(power_power_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),one_one_nat) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_608]) ).

tcf(c_77749,plain,
    hAPP_int_int(plus_plus_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),pls) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_524]) ).

tcf(c_77750,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(cOMBC_int_int_bool(ord_less_int,pls))) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_523]) ).

tcf(c_77751,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(cOMBC_int_int_bool(ord_less_int,pls))) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_347]) ).

tcf(c_77752,plain,
    hAPP_int_int(times_times_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),one_one_int) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_346]) ).

tcf(c_77753,plain,
    number_number_of_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_254]) ).

tcf(c_77757,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_nat_int(power_power_int(X0),iPr_def_11) != iPr_def_18 ) ),
    inference(demodulation,[status(thm)],[c_77730,c_77147]) ).

tcf(c_77764,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( pls != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_77757]) ).

tcf(c_77781,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0)))) = hAPP_int_int(iPr_def_12,number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_12530,c_59636]) ).

tcf(c_77782,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_14))) = hAPP_int_int(iPr_def_12,number_number_of_int(one_one_int)),
    inference(superposition,[status(thm)],[c_59638,c_77781]) ).

tcf(c_77783,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_15))) = hAPP_int_int(iPr_def_12,number_number_of_int(iPr_def_14)),
    inference(superposition,[status(thm)],[c_59639,c_77781]) ).

tcf(c_77784,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_16))) = hAPP_int_int(iPr_def_12,number_number_of_int(iPr_def_15)),
    inference(superposition,[status(thm)],[c_59640,c_77781]) ).

tcf(c_77785,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_18))) = hAPP_int_int(iPr_def_12,number_number_of_int(iPr_def_17)),
    inference(superposition,[status(thm)],[c_59642,c_77781]) ).

tcf(c_77786,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),min))) = hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(min),min))),
    inference(superposition,[status(thm)],[c_76610,c_77781]) ).

tcf(c_77787,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),one_one_int))) = hAPP_int_int(iPr_def_12,number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_77245,c_77781]) ).

tcf(c_77788,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_12,number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0)))) ),
    inference(superposition,[status(thm)],[c_77781,c_58]) ).

tcf(c_77790,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_18))) = iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_77785,c_59642,c_76413]) ).

tcf(c_77791,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_16))) = iPr_def_16,
    inference(light_normalisation,[status(thm)],[c_77784,c_59640,c_76411]) ).

tcf(c_77792,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_15))) = iPr_def_15,
    inference(light_normalisation,[status(thm)],[c_77783,c_59639,c_76410]) ).

tcf(c_77793,plain,
    number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_14))) = iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_77782,c_59638,c_76393]) ).

tcf(c_77796,plain,
    hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(min),min))) = min,
    inference(light_normalisation,[status(thm)],[c_77786,c_76397,c_77141]) ).

tcf(c_77826,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | is_int(sK22(X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_1487]) ).

tcf(c_77827,plain,
    ( is_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
    | ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))) ),
    inference(superposition,[status(thm)],[c_15973,c_1487]) ).

tcf(c_77831,plain,
    is_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_77827,c_61]) ).

tcf(c_77833,plain,
    hAPP_int_int(minus_minus_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),pls) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_880]) ).

tcf(c_77834,plain,
    hAPP_nat_int(power_power_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),one_one_nat) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_608]) ).

tcf(c_77835,plain,
    hAPP_int_int(plus_plus_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),pls) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_524]) ).

tcf(c_77836,plain,
    hAPP_int_int(plus_plus_int(pls),sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_523]) ).

tcf(c_77837,plain,
    hAPP_int_int(times_times_int(one_one_int),sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_347]) ).

tcf(c_77838,plain,
    hAPP_int_int(times_times_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),one_one_int) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_346]) ).

tcf(c_77839,plain,
    number_number_of_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_254]) ).

tcf(c_77847,plain,
    ~ hBOOL(hAPP_int_bool(iPr_def_19,pls)),
    inference(demodulation,[status(thm)],[c_77706,c_1720,c_59643]) ).

tcf(c_77853,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(X1),X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_253,c_76863]) ).

tcf(c_77874,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X1)),pls) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_880]) ).

tcf(c_77875,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),one_one_nat) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_608]) ).

tcf(c_77876,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),pls) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_524]) ).

tcf(c_77877,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_523]) ).

tcf(c_77878,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_347]) ).

tcf(c_77879,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),one_one_int) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_346]) ).

tcf(c_77880,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_254]) ).

tcf(c_77908,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X1),X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_257,c_76880]) ).

tcf(c_77911,plain,
    ! [X0: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_12229,c_76880]) ).

tcf(c_77912,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(t) ),
    inference(superposition,[status(thm)],[c_76316,c_76880]) ).

tcf(c_77913,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(sK9) ),
    inference(superposition,[status(thm)],[c_76325,c_76880]) ).

tcf(c_77929,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_12,X0))
      | ~ is_int(one_one_int) ),
    inference(superposition,[status(thm)],[c_59636,c_76880]) ).

tcf(c_77930,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X1)),pls) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_880]) ).

tcf(c_77931,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X1)),one_one_nat) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_608]) ).

tcf(c_77932,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),pls) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_524]) ).

tcf(c_77933,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_523]) ).

tcf(c_77934,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_347]) ).

tcf(c_77935,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X1)),one_one_int) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_346]) ).

tcf(c_77936,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(X0),X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_254]) ).

tcf(c_77937,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_12,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_77929,c_49]) ).

tcf(c_77940,plain,
    ! [X0: $i] : is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),
    inference(forward_subsumption_resolution,[status(thm)],[c_77911,c_57]) ).

tcf(c_77964,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))) = number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_12841,c_59636]) ).

tcf(c_77965,plain,
    hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(pls)) = number267125858f_real(hAPP_int_int(iPr_def_12,pls)),
    inference(superposition,[status(thm)],[c_340,c_77964]) ).

tcf(c_77966,plain,
    hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(iPr_def_12,one_one_int))) = number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59636,c_77964]) ).

tcf(c_77967,plain,
    hAPP_real_real(plus_plus_real(one_one_real),zero_zero_real) = number267125858f_real(one_one_int),
    inference(light_normalisation,[status(thm)],[c_77965,c_568,c_77245]) ).

tcf(c_77968,plain,
    hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(iPr_def_14)) = number267125858f_real(iPr_def_15),
    inference(light_normalisation,[status(thm)],[c_77966,c_59638,c_59639]) ).

tcf(c_77975,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | is_int(sK23(X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_1488]) ).

tcf(c_77976,plain,
    ( is_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
    | ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))) ),
    inference(superposition,[status(thm)],[c_15973,c_1488]) ).

tcf(c_77980,plain,
    is_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_77976,c_61]) ).

tcf(c_78000,plain,
    ! [X0: $i] : is_int(sK27(X0,t)),
    inference(superposition,[status(thm)],[c_74,c_46404]) ).

tcf(c_78001,plain,
    ! [X0: $i] : is_int(sK27(X0,one_one_int)),
    inference(superposition,[status(thm)],[c_114,c_46404]) ).

tcf(c_78002,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) ),
    inference(superposition,[status(thm)],[c_1563,c_46404]) ).

tcf(c_78003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( is_int(sK27(X3,X1))
      | sP3(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_46418,c_46404]) ).

tcf(c_78018,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X0)),pls) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_880]) ).

tcf(c_78019,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_12,X0)),one_one_nat) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_608]) ).

tcf(c_78020,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),pls) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_524]) ).

tcf(c_78021,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0)) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_523]) ).

tcf(c_78022,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(iPr_def_12,X0)) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_347]) ).

tcf(c_78023,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),one_one_int) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_346]) ).

tcf(c_78024,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(iPr_def_12,X0)) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_77937,c_254]) ).

tcf(c_78025,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0))) = hAPP_int_int(iPr_def_12,number_number_of_int(X0)),
    inference(demodulation,[status(thm)],[c_77781,c_78021]) ).

tcf(c_78026,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,X0))) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)),
    inference(demodulation,[status(thm)],[c_77694,c_78021]) ).

tcf(c_78036,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK27(X0,t)),pls) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_880]) ).

tcf(c_78037,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK27(X0,t)),one_one_nat) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_608]) ).

tcf(c_78038,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK27(X0,t)),pls) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_524]) ).

tcf(c_78039,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK27(X0,t)) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_523]) ).

tcf(c_78040,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK27(X0,t)) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_347]) ).

tcf(c_78041,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK27(X0,t)),one_one_int) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_346]) ).

tcf(c_78042,plain,
    ! [X0: $i] : number_number_of_int(sK27(X0,t)) = sK27(X0,t),
    inference(superposition,[status(thm)],[c_78000,c_254]) ).

tcf(c_78050,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK27(X0,one_one_int)),pls) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_880]) ).

tcf(c_78051,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK27(X0,one_one_int)),one_one_nat) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_608]) ).

tcf(c_78052,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK27(X0,one_one_int)),pls) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_524]) ).

tcf(c_78053,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK27(X0,one_one_int)) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_523]) ).

tcf(c_78054,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK27(X0,one_one_int)) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_347]) ).

tcf(c_78055,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK27(X0,one_one_int)),one_one_int) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_346]) ).

tcf(c_78056,plain,
    ! [X0: $i] : number_number_of_int(sK27(X0,one_one_int)) = sK27(X0,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_254]) ).

tcf(c_78064,plain,
    is_int(number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_340,c_77940]) ).

tcf(c_78065,plain,
    is_int(number_number_of_int(hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59636,c_77940]) ).

tcf(c_78066,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),pls) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_880]) ).

tcf(c_78067,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),one_one_nat) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_608]) ).

tcf(c_78068,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),pls) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_524]) ).

tcf(c_78070,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_347]) ).

tcf(c_78071,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_346]) ).

tcf(c_78072,plain,
    ! [X0: $i] : number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_77940,c_254]) ).

tcf(c_78081,plain,
    hAPP_int_int(minus_minus_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),pls) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_880]) ).

tcf(c_78082,plain,
    hAPP_nat_int(power_power_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),one_one_nat) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_608]) ).

tcf(c_78083,plain,
    hAPP_int_int(plus_plus_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),pls) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_524]) ).

tcf(c_78084,plain,
    hAPP_int_int(plus_plus_int(pls),sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_523]) ).

tcf(c_78085,plain,
    hAPP_int_int(times_times_int(one_one_int),sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_347]) ).

tcf(c_78086,plain,
    hAPP_int_int(times_times_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),one_one_int) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_346]) ).

tcf(c_78087,plain,
    number_number_of_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_254]) ).

tcf(c_78089,plain,
    hAPP_int_int(iPr_def_12,one_one_int) != one_one_int,
    inference(superposition,[status(thm)],[c_59636,c_77377]) ).

tcf(c_78090,plain,
    one_one_int != iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_78089,c_59638]) ).

tcf(c_78095,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_int_int(minus_minus_int(sK15(X0,X1)),pls) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_880]) ).

tcf(c_78096,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_nat_int(power_power_int(sK15(X0,X1)),one_one_nat) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_608]) ).

tcf(c_78097,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_int_int(plus_plus_int(sK15(X0,X1)),pls) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_524]) ).

tcf(c_78098,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_int_int(plus_plus_int(pls),sK15(X0,X1)) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_523]) ).

tcf(c_78099,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_int_int(times_times_int(one_one_int),sK15(X0,X1)) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_347]) ).

tcf(c_78100,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( hAPP_int_int(times_times_int(sK15(X0,X1)),one_one_int) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_346]) ).

tcf(c_78101,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(quadRes(X0)))
      | ( number_number_of_int(sK15(X0,X1)) = sK15(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_77479,c_254]) ).

tcf(c_78124,plain,
    number267125858f_real(one_one_int) = one_one_real,
    inference(demodulation,[status(thm)],[c_77967,c_516]) ).

tcf(c_78125,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_12842,c_59636]) ).

tcf(c_78126,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_78125,c_78024]) ).

tcf(c_78127,plain,
    hAPP_int_int(iPr_def_12,number_number_of_int(pls)) = hAPP_int_int(iPr_def_12,pls),
    inference(superposition,[status(thm)],[c_340,c_78126]) ).

tcf(c_78128,plain,
    hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(iPr_def_12,one_one_int))) = hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_78126]) ).

tcf(c_78129,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_78126,c_65]) ).

tcf(c_78130,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_78126,c_77937]) ).

tcf(c_78131,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(superposition,[status(thm)],[c_78126,c_76515]) ).

tcf(c_78132,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != pls,
    inference(superposition,[status(thm)],[c_78126,c_76368]) ).

tcf(c_78137,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_12,X0)))
      | ~ is_int(X0) ),
    inference(light_normalisation,[status(thm)],[c_279,c_76874]) ).

tcf(c_78144,plain,
    ( hBOOL(hAPP_int_bool(iPr_def_19,hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ is_int(one_one_int) ),
    inference(superposition,[status(thm)],[c_59643,c_78137]) ).

tcf(c_78145,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),iPr_def_14))
    | ~ is_int(one_one_int) ),
    inference(superposition,[status(thm)],[c_59638,c_78137]) ).

tcf(c_78146,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),iPr_def_15))
    | ~ is_int(iPr_def_14) ),
    inference(superposition,[status(thm)],[c_59639,c_78137]) ).

tcf(c_78147,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),iPr_def_16))
    | ~ is_int(iPr_def_15) ),
    inference(superposition,[status(thm)],[c_59640,c_78137]) ).

tcf(c_78148,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),iPr_def_18))
    | ~ is_int(iPr_def_17) ),
    inference(superposition,[status(thm)],[c_59642,c_78137]) ).

tcf(c_78149,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(min),min)),min))
    | ~ is_int(hAPP_int_int(plus_plus_int(min),min)) ),
    inference(superposition,[status(thm)],[c_76610,c_78137]) ).

tcf(c_78151,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_78126,c_78137]) ).

tcf(c_78152,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),hAPP_i1948725293t_bool(ord_less_int,X0)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_78137,c_226]) ).

tcf(c_78153,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),iPr_def_18)),
    inference(forward_subsumption_resolution,[status(thm)],[c_78148,c_76349]) ).

tcf(c_78154,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),iPr_def_16)),
    inference(forward_subsumption_resolution,[status(thm)],[c_78147,c_76347]) ).

tcf(c_78155,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),iPr_def_15)),
    inference(forward_subsumption_resolution,[status(thm)],[c_78146,c_76346]) ).

tcf(c_78156,plain,
    ( hBOOL(hAPP_int_bool(iPr_def_19,iPr_def_14))
    | ~ is_int(one_one_int) ),
    inference(light_normalisation,[status(thm)],[c_78145,c_59643]) ).

tcf(c_78157,plain,
    hBOOL(hAPP_int_bool(iPr_def_19,iPr_def_14)),
    inference(forward_subsumption_resolution,[status(thm)],[c_78156,c_49]) ).

tcf(c_78164,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_78151,c_77940]) ).

tcf(c_78179,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),X1) != X1 ) ),
    inference(superposition,[status(thm)],[c_243,c_517]) ).

tcf(c_78183,plain,
    ! [X0: $i] :
      ( ( number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)) = zero_zero_real )
      | ( number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != one_one_real ) ),
    inference(superposition,[status(thm)],[c_77964,c_517]) ).

tcf(c_78195,plain,
    hBOOL(member_int(iPr_def_14,iPr_def_19)),
    inference(superposition,[status(thm)],[c_78157,c_226]) ).

tcf(c_78196,plain,
    is_int(sK26(iPr_def_14)),
    inference(superposition,[status(thm)],[c_78157,c_77637]) ).

tcf(c_78197,plain,
    hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),pls) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_880]) ).

tcf(c_78198,plain,
    hAPP_nat_int(power_power_int(sK26(iPr_def_14)),one_one_nat) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_608]) ).

tcf(c_78199,plain,
    hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),pls) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_524]) ).

tcf(c_78200,plain,
    hAPP_int_int(plus_plus_int(pls),sK26(iPr_def_14)) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_523]) ).

tcf(c_78201,plain,
    hAPP_int_int(times_times_int(one_one_int),sK26(iPr_def_14)) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_347]) ).

tcf(c_78202,plain,
    hAPP_int_int(times_times_int(sK26(iPr_def_14)),one_one_int) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_346]) ).

tcf(c_78203,plain,
    number_number_of_int(sK26(iPr_def_14)) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_254]) ).

tcf(c_78205,plain,
    hBOOL(member_int(iPr_def_18,hAPP_i1948725293t_bool(ord_less_int,iPr_def_17))),
    inference(superposition,[status(thm)],[c_78153,c_226]) ).

tcf(c_78206,plain,
    hBOOL(member_int(iPr_def_16,hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),
    inference(superposition,[status(thm)],[c_78154,c_226]) ).

tcf(c_78207,plain,
    hBOOL(member_int(iPr_def_15,hAPP_i1948725293t_bool(ord_less_int,iPr_def_14))),
    inference(superposition,[status(thm)],[c_78155,c_226]) ).

tcf(c_78216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_int_int(minus_minus_int(sK27(X0,X1)),pls) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_880]) ).

tcf(c_78217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_nat_int(power_power_int(sK27(X0,X1)),one_one_nat) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_608]) ).

tcf(c_78218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_int_int(plus_plus_int(sK27(X0,X1)),pls) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_524]) ).

tcf(c_78219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_int_int(plus_plus_int(pls),sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_523]) ).

tcf(c_78220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_int_int(times_times_int(one_one_int),sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_347]) ).

tcf(c_78221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( hAPP_int_int(times_times_int(sK27(X0,X1)),one_one_int) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_346]) ).

tcf(c_78222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X2,X1,X3)
      | ( number_number_of_int(sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78003,c_254]) ).

tcf(c_78250,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),X0)),hAPP_int_int(minus_minus_int(min),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_13390,c_59636]) ).

tcf(c_78251,plain,
    hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(pls),pls))) = hAPP_int_int(plus_plus_int(min),min),
    inference(superposition,[status(thm)],[c_77407,c_78250]) ).

tcf(c_78253,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_78250,c_78126]) ).

tcf(c_78254,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != one_one_int,
    inference(superposition,[status(thm)],[c_78250,c_77377]) ).

tcf(c_78255,plain,
    ! [X0: $i] : is_int(number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_78250,c_77940]) ).

tcf(c_78256,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_78250,c_77964]) ).

tcf(c_78257,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_78250,c_12229]) ).

tcf(c_78258,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != iPr_def_15,
    inference(superposition,[status(thm)],[c_78250,c_76521]) ).

tcf(c_78259,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != min,
    inference(superposition,[status(thm)],[c_78250,c_755]) ).

tcf(c_78260,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(hAPP_int_int(minus_minus_int(min),X0)) ),
    inference(superposition,[status(thm)],[c_78250,c_65]) ).

tcf(c_78262,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) != hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_12,X1)),
    inference(superposition,[status(thm)],[c_78250,c_76515]) ).

tcf(c_78263,plain,
    hAPP_int_int(plus_plus_int(min),min) = hAPP_int_int(minus_minus_int(min),one_one_int),
    inference(light_normalisation,[status(thm)],[c_78251,c_340,c_77245]) ).

tcf(c_78280,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ( number_number_of_nat(X0) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1563,c_811]) ).

tcf(c_78281,plain,
    ! [X0: $i,X1: $i] :
      ( sP3(X0,pls,X1)
      | ( number_number_of_nat(one_one_int) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_46418,c_811]) ).

tcf(c_78282,plain,
    number_number_of_nat(min) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_774,c_811]) ).

tcf(c_78293,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),X0)),X0)),
    inference(superposition,[status(thm)],[c_253,c_833]) ).

tcf(c_78295,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),X1)),X1)),
    inference(superposition,[status(thm)],[c_1004,c_833]) ).

tcf(c_78296,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),pls)),pls)),
    inference(superposition,[status(thm)],[c_1001,c_833]) ).

tcf(c_78297,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(one_one_int,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_2495,c_833]) ).

tcf(c_78298,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,X0),hAPP_int_int(times_times_int(X1),m)),m)),
    inference(superposition,[status(thm)],[c_76855,c_833]) ).

tcf(c_78299,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(iPr_def_14,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_76924,c_833]) ).

tcf(c_78300,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(iPr_def_15,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_76925,c_833]) ).

tcf(c_78301,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(iPr_def_16,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_76926,c_833]) ).

tcf(c_78302,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(iPr_def_17,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_76927,c_833]) ).

tcf(c_78303,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(iPr_def_18,hAPP_int_int(times_times_int(X0),one_one_int)),one_one_int)),
    inference(superposition,[status(thm)],[c_76928,c_833]) ).

tcf(c_78304,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(min,hAPP_int_int(times_times_int(X0),min)),min)),
    inference(superposition,[status(thm)],[c_76977,c_833]) ).

tcf(c_78305,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(s1,hAPP_int_int(times_times_int(X0),s1)),s1)),
    inference(superposition,[status(thm)],[c_76983,c_833]) ).

tcf(c_78306,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(s,hAPP_int_int(times_times_int(X0),s)),s)),
    inference(superposition,[status(thm)],[c_76989,c_833]) ).

tcf(c_78307,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_833]) ).

tcf(c_78308,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(t,hAPP_int_int(times_times_int(X0),t)),t)),
    inference(superposition,[status(thm)],[c_77001,c_833]) ).

tcf(c_78309,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK9,hAPP_int_int(times_times_int(X0),sK9)),sK9)),
    inference(superposition,[status(thm)],[c_77007,c_833]) ).

tcf(c_78310,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK10,hAPP_int_int(times_times_int(X0),sK10)),sK10)),
    inference(superposition,[status(thm)],[c_77013,c_833]) ).

tcf(c_78311,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK11,hAPP_int_int(times_times_int(X0),sK11)),sK11)),
    inference(superposition,[status(thm)],[c_77019,c_833]) ).

tcf(c_78312,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK13,hAPP_int_int(times_times_int(X0),sK13)),sK13)),
    inference(superposition,[status(thm)],[c_77025,c_833]) ).

tcf(c_78313,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,X0),hAPP_int_int(times_times_int(X1),X0)),X0)),
    inference(superposition,[status(thm)],[c_59637,c_833]) ).

tcf(c_78314,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X1),X2)),X1)),
    inference(superposition,[status(thm)],[c_253,c_833]) ).

tcf(c_78316,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),pls),X1)),
    inference(superposition,[status(thm)],[c_1004,c_833]) ).

tcf(c_78317,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),pls),pls),pls)),
    inference(superposition,[status(thm)],[c_1001,c_833]) ).

tcf(c_78318,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),one_one_int),one_one_int)),
    inference(superposition,[status(thm)],[c_2495,c_833]) ).

tcf(c_78319,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),m),hAPP_int_int(iPr_def_13,X1)),m)),
    inference(superposition,[status(thm)],[c_76855,c_833]) ).

tcf(c_78320,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),iPr_def_14),one_one_int)),
    inference(superposition,[status(thm)],[c_76924,c_833]) ).

tcf(c_78321,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),iPr_def_15),one_one_int)),
    inference(superposition,[status(thm)],[c_76925,c_833]) ).

tcf(c_78322,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),iPr_def_16),one_one_int)),
    inference(superposition,[status(thm)],[c_76926,c_833]) ).

tcf(c_78323,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),iPr_def_17),one_one_int)),
    inference(superposition,[status(thm)],[c_76927,c_833]) ).

tcf(c_78324,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),one_one_int),iPr_def_18),one_one_int)),
    inference(superposition,[status(thm)],[c_76928,c_833]) ).

tcf(c_78325,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),min),min),min)),
    inference(superposition,[status(thm)],[c_76977,c_833]) ).

tcf(c_78326,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),s1),s1),s1)),
    inference(superposition,[status(thm)],[c_76983,c_833]) ).

tcf(c_78327,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),s),s),s)),
    inference(superposition,[status(thm)],[c_76989,c_833]) ).

tcf(c_78328,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_833]) ).

tcf(c_78329,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),t),t),t)),
    inference(superposition,[status(thm)],[c_77001,c_833]) ).

tcf(c_78330,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK9),sK9),sK9)),
    inference(superposition,[status(thm)],[c_77007,c_833]) ).

tcf(c_78331,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK10),sK10),sK10)),
    inference(superposition,[status(thm)],[c_77013,c_833]) ).

tcf(c_78332,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK11),sK11),sK11)),
    inference(superposition,[status(thm)],[c_77019,c_833]) ).

tcf(c_78333,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK13),sK13),sK13)),
    inference(superposition,[status(thm)],[c_77025,c_833]) ).

tcf(c_78334,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(iPr_def_13,X1)),X1)),
    inference(superposition,[status(thm)],[c_59637,c_833]) ).

tcf(c_78335,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X1),X0),hAPP_int_int(times_times_int(X2),X0)))),
    inference(superposition,[status(thm)],[c_833,c_226]) ).

tcf(c_78336,plain,
    hBOOL(hAPP_int_bool(zcong(pls,pls),pls)),
    inference(light_normalisation,[status(thm)],[c_78317,c_1001]) ).

tcf(c_78338,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,X0),hAPP_int_int(iPr_def_13,X1)),m)),
    inference(light_normalisation,[status(thm)],[c_78319,c_76855]) ).

tcf(c_78394,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),X0) = hAPP_int_int(iPr_def_12,X0),
    inference(superposition,[status(thm)],[c_76874,c_257]) ).

tcf(c_78397,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_253,c_78307]) ).

tcf(c_78399,plain,
    hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_1004,c_78307]) ).

tcf(c_78400,plain,
    hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_78307]) ).

tcf(c_78401,plain,
    hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59637,c_78307]) ).

tcf(c_78402,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_78307,c_226]) ).

tcf(c_78405,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_253,c_78328]) ).

tcf(c_78407,plain,
    hBOOL(hAPP_int_bool(zcong(pls,sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_1004,c_78328]) ).

tcf(c_78409,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59637,c_78328]) ).

tcf(c_78410,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_78328,c_226]) ).

tcf(c_78413,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(pls,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_78407,c_226]) ).

tcf(c_78414,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_78401,c_226]) ).

tcf(c_78415,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_78409,c_226]) ).

tcf(c_78420,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),
    inference(superposition,[status(thm)],[c_78397,c_226]) ).

tcf(c_78424,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),pls))),
    inference(superposition,[status(thm)],[c_1004,c_78402]) ).

tcf(c_78425,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76995,c_78402]) ).

tcf(c_78432,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_78405,c_226]) ).

tcf(c_78434,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(light_normalisation,[status(thm)],[c_13391,c_59636]) ).

tcf(c_78435,plain,
    hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(min),min)) = hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),min)),
    inference(superposition,[status(thm)],[c_76610,c_78434]) ).

tcf(c_78437,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,pls))) = hAPP_int_int(minus_minus_int(min),pls),
    inference(superposition,[status(thm)],[c_340,c_78434]) ).

tcf(c_78438,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_78250,c_78434]) ).

tcf(c_78439,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int)))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_78434]) ).

tcf(c_78441,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(superposition,[status(thm)],[c_78434,c_78137]) ).

tcf(c_78442,plain,
    ! [X0: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_78434,c_77937]) ).

tcf(c_78443,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(superposition,[status(thm)],[c_78434,c_76515]) ).

tcf(c_78444,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) != pls,
    inference(superposition,[status(thm)],[c_78434,c_76368]) ).

tcf(c_78446,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),iPr_def_15)) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(light_normalisation,[status(thm)],[c_78439,c_59638,c_59639]) ).

tcf(c_78447,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_78438,c_78434]) ).

tcf(c_78477,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X1 ) ),
    inference(superposition,[status(thm)],[c_1284,c_1321]) ).

tcf(c_78481,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(iPr_def_10,X0) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_59634,c_1321]) ).

tcf(c_78495,plain,
    ! [X0: $i] :
      ( ( one_one_nat = zero_zero_nat )
      | ( hAPP_nat_nat(iPr_def_10,X0) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_59634,c_1323]) ).

tcf(c_78496,plain,
    ! [X0: $i] : hAPP_nat_nat(iPr_def_10,X0) != zero_zero_nat,
    inference(forward_subsumption_resolution,[status(thm)],[c_78495,c_1009]) ).

tcf(c_78498,plain,
    zero_zero_nat != iPr_def_11,
    inference(superposition,[status(thm)],[c_59635,c_78496]) ).

tcf(c_78500,plain,
    pls != iPr_def_18,
    inference(backward_subsumption_resolution,[status(thm)],[c_77764,c_78498]) ).

tcf(c_78501,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(X0),iPr_def_11) != iPr_def_18,
    inference(backward_subsumption_resolution,[status(thm)],[c_77757,c_78498]) ).

tcf(c_78502,plain,
    one_one_int != iPr_def_18,
    inference(backward_subsumption_resolution,[status(thm)],[c_77732,c_78498]) ).

tcf(c_78526,plain,
    is_int(hAPP_int_int(minus_minus_int(min),pls)),
    inference(superposition,[status(thm)],[c_340,c_78442]) ).

tcf(c_78527,plain,
    ! [X0: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_78250,c_78442]) ).

tcf(c_78528,plain,
    is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59636,c_78442]) ).

tcf(c_78529,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_880]) ).

tcf(c_78530,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),one_one_nat) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_608]) ).

tcf(c_78531,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_524]) ).

tcf(c_78532,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_523]) ).

tcf(c_78533,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_347]) ).

tcf(c_78534,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),one_one_int) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_346]) ).

tcf(c_78535,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_78442,c_254]) ).

tcf(c_78537,plain,
    is_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_78528,c_59638]) ).

tcf(c_78538,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(light_normalisation,[status(thm)],[c_78527,c_78447]) ).

tcf(c_78546,plain,
    number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),iPr_def_14))))) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_13926,c_59634,c_59635,c_59636,c_59638]) ).

tcf(c_78547,plain,
    number_number_of_nat(iPr_def_14) = iPr_def_11,
    inference(demodulation,[status(thm)],[c_78546,c_257,c_76727]) ).

tcf(c_78558,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(times_times_nat(one_one_nat),one_one_nat))),
    inference(superposition,[status(thm)],[c_1417,c_1408]) ).

tcf(c_78586,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)),pls) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_880]) ).

tcf(c_78587,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)),one_one_nat) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_608]) ).

tcf(c_78588,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)),pls) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_524]) ).

tcf(c_78589,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(min),iPr_def_14)) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_523]) ).

tcf(c_78590,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(min),iPr_def_14)) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_347]) ).

tcf(c_78591,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)),one_one_int) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_346]) ).

tcf(c_78592,plain,
    number_number_of_int(hAPP_int_int(minus_minus_int(min),iPr_def_14)) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(superposition,[status(thm)],[c_78537,c_254]) ).

tcf(c_78594,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,undefined_int(int)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_77063,c_1042]) ).

tcf(c_78595,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(undefined_int(int),hAPP_int_int(times_times_int(X0),undefined_int(int))),undefined_int(int))),
    inference(superposition,[status(thm)],[c_77063,c_833]) ).

tcf(c_78597,plain,
    hBOOL(member_int(undefined_int(int),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77063,c_76535]) ).

tcf(c_78598,plain,
    hBOOL(member_int(undefined_int(int),hAPP_i1948725293t_bool(dvd_dvd_int,undefined_int(int)))),
    inference(superposition,[status(thm)],[c_77063,c_76498]) ).

tcf(c_78599,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),undefined_int(int))),
    inference(superposition,[status(thm)],[c_77063,c_1045]) ).

tcf(c_78600,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),undefined_int(int)),undefined_int(int)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_77063,c_833]) ).

tcf(c_78604,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,twoSqu1241645765sum2sq(X0)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_77069,c_1042]) ).

tcf(c_78605,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(twoSqu1241645765sum2sq(X0),hAPP_int_int(times_times_int(X1),twoSqu1241645765sum2sq(X0))),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_77069,c_833]) ).

tcf(c_78607,plain,
    ! [X0: $i] : hBOOL(member_int(twoSqu1241645765sum2sq(X0),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_77069,c_76535]) ).

tcf(c_78608,plain,
    ! [X0: $i] : hBOOL(member_int(twoSqu1241645765sum2sq(X0),hAPP_i1948725293t_bool(dvd_dvd_int,twoSqu1241645765sum2sq(X0)))),
    inference(superposition,[status(thm)],[c_77069,c_76498]) ).

tcf(c_78609,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_77069,c_1045]) ).

tcf(c_78610,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),twoSqu1241645765sum2sq(X1)),twoSqu1241645765sum2sq(X1)),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_77069,c_833]) ).

tcf(c_78625,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(light_normalisation,[status(thm)],[c_14189,c_59636]) ).

tcf(c_78626,plain,
    hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(min),min)) = hAPP_int_int(minus_minus_int(pls),min),
    inference(superposition,[status(thm)],[c_76610,c_78625]) ).

tcf(c_78628,plain,
    hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,pls)) = hAPP_int_int(minus_minus_int(min),pls),
    inference(superposition,[status(thm)],[c_340,c_78625]) ).

tcf(c_78629,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_78250,c_78625]) ).

tcf(c_78630,plain,
    hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_78625]) ).

tcf(c_78632,plain,
    hAPP_int_int(minus_minus_int(pls),one_one_int) = min,
    inference(light_normalisation,[status(thm)],[c_78628,c_77245,c_77407]) ).

tcf(c_78633,plain,
    hAPP_int_int(minus_minus_int(pls),iPr_def_15) = hAPP_int_int(minus_minus_int(min),iPr_def_14),
    inference(light_normalisation,[status(thm)],[c_78630,c_59638,c_59639]) ).

tcf(c_78634,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(minus_minus_int(pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_78629,c_78434,c_78447]) ).

tcf(c_78635,plain,
    is_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),
    inference(demodulation,[status(thm)],[c_78537,c_78633]) ).

tcf(c_78637,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zprime,sK26(X0)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_1510,c_59643]) ).

tcf(c_78644,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(sK26(X0),zprime))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(superposition,[status(thm)],[c_78637,c_226]) ).

tcf(c_78652,plain,
    zfact(pls) = one_one_int,
    inference(superposition,[status(thm)],[c_114,c_1519]) ).

tcf(c_78653,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ( zfact(X0) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_1563,c_1519]) ).

tcf(c_78654,plain,
    ! [X0: $i,X1: $i] :
      ( sP3(X0,pls,X1)
      | ( zfact(one_one_int) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_46418,c_1519]) ).

tcf(c_78655,plain,
    zfact(min) = one_one_int,
    inference(superposition,[status(thm)],[c_774,c_1519]) ).

tcf(c_78661,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(member_int(X0,d22set(X1))) ),
    inference(light_normalisation,[status(thm)],[c_1580,c_59643]) ).

tcf(c_78668,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X1))
      | is_int(sK30(d22set(X0))) ),
    inference(superposition,[status(thm)],[c_76445,c_78661]) ).

tcf(c_78676,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(X0))
      | sP3(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_1563,c_1647]) ).

tcf(c_78677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1,X2)
      | sP3(X0,sK39(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_46418,c_1647]) ).

tcf(c_78678,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP3(zcong(X0,X0),X1,X2),
    inference(superposition,[status(thm)],[c_815,c_1647]) ).

tcf(c_78679,plain,
    ! [X0: $i,X1: $i] : sP3(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X0,X1),
    inference(superposition,[status(thm)],[c_1051,c_1647]) ).

tcf(c_78688,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),pls) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_880]) ).

tcf(c_78689,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),one_one_nat) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_608]) ).

tcf(c_78690,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),pls) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_524]) ).

tcf(c_78691,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(pls),iPr_def_15)) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_523]) ).

tcf(c_78692,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(pls),iPr_def_15)) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_347]) ).

tcf(c_78693,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),one_one_int) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_346]) ).

tcf(c_78694,plain,
    number_number_of_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_254]) ).

tcf(c_78712,plain,
    ! [X0: $i] : is_int(sK30(d22set(X0))),
    inference(superposition,[status(thm)],[c_78668,c_77847]) ).

tcf(c_78721,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK30(d22set(X0))),pls) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_880]) ).

tcf(c_78722,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK30(d22set(X0))),one_one_nat) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_608]) ).

tcf(c_78723,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(d22set(X0))),pls) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_524]) ).

tcf(c_78724,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK30(d22set(X0))) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_523]) ).

tcf(c_78725,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK30(d22set(X0))) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_347]) ).

tcf(c_78726,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(d22set(X0))),one_one_int) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_346]) ).

tcf(c_78727,plain,
    ! [X0: $i] : number_number_of_int(sK30(d22set(X0))) = sK30(d22set(X0)),
    inference(superposition,[status(thm)],[c_78712,c_254]) ).

tcf(c_78742,plain,
    ! [X0: $i] :
      ( ( one_one_nat = zero_zero_nat )
      | ( hAPP_nat_nat(iPr_def_10,X0) != X0 ) ),
    inference(superposition,[status(thm)],[c_77521,c_1321]) ).

tcf(c_78746,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(iPr_def_10,X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_77521,c_1327]) ).

tcf(c_78752,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(one_one_nat),X0) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_77521,c_1284]) ).

tcf(c_78756,plain,
    ! [X0: $i] : hAPP_nat_nat(iPr_def_10,X0) != X0,
    inference(forward_subsumption_resolution,[status(thm)],[c_78742,c_1009]) ).

tcf(c_78759,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),X1)),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))),X0),
    inference(light_normalisation,[status(thm)],[c_14225,c_59636]) ).

tcf(c_78760,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),one_one_int) = hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_78759]) ).

tcf(c_78761,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))),X0),
    inference(superposition,[status(thm)],[c_253,c_78759]) ).

tcf(c_78763,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),pls) = hAPP_int_int(plus_plus_int(pls),pls),
    inference(superposition,[status(thm)],[c_1001,c_78759]) ).

tcf(c_78764,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),m) = hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_76855,c_78759]) ).

tcf(c_78766,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(pls),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,pls)),X0),
    inference(superposition,[status(thm)],[c_340,c_78759]) ).

tcf(c_78767,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))))),X0),
    inference(superposition,[status(thm)],[c_78250,c_78759]) ).

tcf(c_78768,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int))),X0),
    inference(superposition,[status(thm)],[c_59636,c_78759]) ).

tcf(c_78769,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),X1))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_78759,c_65]) ).

tcf(c_78770,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))),X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_78759,c_76880]) ).

tcf(c_78773,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),pls) = hAPP_int_int(times_times_int(one_one_int),X0),
    inference(light_normalisation,[status(thm)],[c_78766,c_1004,c_77245]) ).

tcf(c_78774,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),pls) = pls,
    inference(light_normalisation,[status(thm)],[c_78763,c_340]) ).

tcf(c_78777,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X0)) = hAPP_int_int(times_times_int(iPr_def_15),X0),
    inference(light_normalisation,[status(thm)],[c_78768,c_59638,c_59639]) ).

tcf(c_78814,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
      | ~ sP4(hAPP_nat_nat(times_times_nat(X0),X1),X2,X0) ),
    inference(superposition,[status(thm)],[c_1684,c_1711]) ).

tcf(c_78815,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ sP4(X0,X1,X0) ),
    inference(superposition,[status(thm)],[c_77669,c_1711]) ).

tcf(c_78816,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
      | ~ sP4(X0,X1,one_one_nat) ),
    inference(superposition,[status(thm)],[c_77670,c_1711]) ).

tcf(c_78817,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ sP4(zero_zero_nat,X0,X1) ),
    inference(superposition,[status(thm)],[c_77672,c_1711]) ).

tcf(c_78818,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat )
      | ~ sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X1) ),
    inference(superposition,[status(thm)],[c_1711,c_1590]) ).

tcf(c_78819,plain,
    ! [X0: $i,X1: $i] : ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1),
    inference(superposition,[status(thm)],[c_1711,c_1358]) ).

tcf(c_78820,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X2)),X1),
    inference(superposition,[status(thm)],[c_1711,c_1343]) ).

tcf(c_78821,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(div_mod_nat(X0),X2))),X2),
    inference(superposition,[status(thm)],[c_1711,c_1344]) ).

tcf(c_78848,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1330,c_1712]) ).

tcf(c_78849,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)
      | ( hAPP_nat_nat(div_mod_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1712]) ).

tcf(c_78850,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1),
    inference(superposition,[status(thm)],[c_1282,c_1712]) ).

tcf(c_78851,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X1),
    inference(superposition,[status(thm)],[c_1594,c_1712]) ).

tcf(c_78852,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X1),
    inference(superposition,[status(thm)],[c_1365,c_1712]) ).

tcf(c_78853,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1295,c_1712]) ).

tcf(c_78854,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X2)),X1),
    inference(superposition,[status(thm)],[c_1299,c_1712]) ).

tcf(c_78855,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X2)),X1),
    inference(superposition,[status(thm)],[c_1694,c_1712]) ).

tcf(c_78857,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(times_times_nat(X1),X2),X0,X1)
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1684,c_1712]) ).

tcf(c_78858,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,X0,X1)
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_77669,c_1712]) ).

tcf(c_78859,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,X0,one_one_nat)
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_77670,c_1712]) ).

tcf(c_78860,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(zero_zero_nat,X0,X1)
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_77672,c_1712]) ).

tcf(c_78893,plain,
    one_one_nat != iPr_def_11,
    inference(superposition,[status(thm)],[c_59635,c_78756]) ).

tcf(c_78900,plain,
    hAPP_nat_nat(minus_minus_nat(iPr_def_11),one_one_nat) = one_one_nat,
    inference(superposition,[status(thm)],[c_59635,c_77538]) ).

tcf(c_78901,plain,
    hAPP_nat_nat(minus_minus_nat(one_one_nat),zero_zero_nat) = one_one_nat,
    inference(superposition,[status(thm)],[c_76367,c_77538]) ).

tcf(c_78904,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(plus_plus_nat(X1),X0)) = hAPP_nat_nat(minus_minus_nat(one_one_nat),X1),
    inference(superposition,[status(thm)],[c_77538,c_11972]) ).

tcf(c_78909,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(iPr_def_11),hAPP_nat_nat(plus_plus_nat(X0),one_one_nat)) = hAPP_nat_nat(minus_minus_nat(one_one_nat),X0),
    inference(superposition,[status(thm)],[c_78900,c_11972]) ).

tcf(c_78910,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(iPr_def_11),hAPP_nat_nat(iPr_def_10,X0)) = hAPP_nat_nat(minus_minus_nat(one_one_nat),X0),
    inference(light_normalisation,[status(thm)],[c_78909,c_77521]) ).

tcf(c_78913,plain,
    hAPP_nat_nat(minus_minus_nat(one_one_nat),one_one_nat) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_76367,c_77549]) ).

tcf(c_78916,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_77549,c_11972]) ).

tcf(c_78918,plain,
    hAPP_nat_nat(minus_minus_nat(one_one_nat),iPr_def_11) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_59635,c_77596]) ).

tcf(c_78922,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(iPr_def_10,X1))) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0),
    inference(superposition,[status(thm)],[c_77596,c_11972]) ).

tcf(c_78923,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(iPr_def_10,X1))) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_78922,c_1244]) ).

tcf(c_78927,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(X0),iPr_def_11)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0),
    inference(superposition,[status(thm)],[c_78918,c_11972]) ).

tcf(c_78928,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(X0),iPr_def_11)) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_78927,c_1244]) ).

tcf(c_78930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_78764,c_76855]) ).

tcf(c_78932,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,pls)) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,pls)),
    inference(superposition,[status(thm)],[c_340,c_78930]) ).

tcf(c_78933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_78250,c_78930]) ).

tcf(c_78934,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,one_one_int))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59636,c_78930]) ).

tcf(c_78935,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_78930,c_65]) ).

tcf(c_78936,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_78930,c_76880]) ).

tcf(c_78938,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,iPr_def_14)) = hAPP_int_int(iPr_def_13,iPr_def_15),
    inference(light_normalisation,[status(thm)],[c_78934,c_59638,c_59639]) ).

tcf(c_78939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_78933,c_78434]) ).

tcf(c_78941,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X1,hAPP_i1948725293t_bool(X0,X2)))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_226]) ).

tcf(c_78942,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(X0,X2)))
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_1563]) ).

tcf(c_78944,plain,
    ! [X0: $i] :
      ( ( zfact(X0) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_1519]) ).

tcf(c_78945,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_811]) ).

tcf(c_78946,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,pls),X0)),
    inference(superposition,[status(thm)],[c_1720,c_954]) ).

tcf(c_78947,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(X1,cOMBC_int_int_bool(X0,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_226]) ).

tcf(c_78948,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(cOMBC_int_int_bool(X0,X2)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_1563]) ).

tcf(c_78968,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
    inference(superposition,[status(thm)],[c_609,c_14104]) ).

tcf(c_78969,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real)),
    inference(superposition,[status(thm)],[c_782,c_14104]) ).

tcf(c_78970,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_14195,c_59634,c_59635]) ).

tcf(c_78971,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ( zero_zero_nat = iPr_def_11 ) ),
    inference(superposition,[status(thm)],[c_491,c_78970]) ).

tcf(c_78973,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_nat_int(power_power_int(X0),iPr_def_11),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_78970,c_226]) ).

tcf(c_78976,plain,
    ! [X0: $i] : hBOOL(member_int(X0,cOMBC_int_int_bool(dvd_dvd_int,pls))),
    inference(superposition,[status(thm)],[c_78946,c_226]) ).

tcf(c_78978,plain,
    ! [X0: $i,X1: $i] : sP3(cOMBC_int_int_bool(dvd_dvd_int,pls),X0,X1),
    inference(superposition,[status(thm)],[c_78946,c_1647]) ).

tcf(c_78984,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),one_one_nat)),
    inference(superposition,[status(thm)],[c_59635,c_77608]) ).

tcf(c_78985,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),one_one_nat)),
    inference(superposition,[status(thm)],[c_76367,c_77608]) ).

tcf(c_78986,plain,
    ! [X0: $i,X1: $i] : ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(div_mod_nat(X0),X1))),X1),
    inference(superposition,[status(thm)],[c_1711,c_77614]) ).

tcf(c_78988,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
    inference(superposition,[status(thm)],[c_76367,c_77614]) ).

tcf(c_78997,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(minus_minus_int(sK22(X0)),pls) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_880]) ).

tcf(c_78998,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_nat_int(power_power_int(sK22(X0)),one_one_nat) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_608]) ).

tcf(c_78999,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(sK22(X0)),pls) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_524]) ).

tcf(c_79000,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(pls),sK22(X0)) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_523]) ).

tcf(c_79001,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(times_times_int(one_one_int),sK22(X0)) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_347]) ).

tcf(c_79002,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(times_times_int(sK22(X0)),one_one_int) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_346]) ).

tcf(c_79003,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( number_number_of_int(sK22(X0)) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_254]) ).

tcf(c_79032,plain,
    ( ( number267125858f_real(iPr_def_14) = zero_zero_real )
    | ( number267125858f_real(iPr_def_15) != one_one_real ) ),
    inference(superposition,[status(thm)],[c_77968,c_517]) ).

tcf(c_79041,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(minus_minus_int(sK23(X0)),pls) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_880]) ).

tcf(c_79042,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_nat_int(power_power_int(sK23(X0)),one_one_nat) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_608]) ).

tcf(c_79043,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(sK23(X0)),pls) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_524]) ).

tcf(c_79044,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(pls),sK23(X0)) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_523]) ).

tcf(c_79045,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(times_times_int(one_one_int),sK23(X0)) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_347]) ).

tcf(c_79046,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(times_times_int(sK23(X0)),one_one_int) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_346]) ).

tcf(c_79047,plain,
    ! [X0: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( number_number_of_int(sK23(X0)) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_254]) ).

tcf(c_79080,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(minus_minus_int(sK27(X0,X1)),pls) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_880]) ).

tcf(c_79081,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_nat_int(power_power_int(sK27(X0,X1)),one_one_nat) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_608]) ).

tcf(c_79082,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(plus_plus_int(sK27(X0,X1)),pls) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_524]) ).

tcf(c_79083,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(plus_plus_int(pls),sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_523]) ).

tcf(c_79084,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(times_times_int(one_one_int),sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_347]) ).

tcf(c_79085,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(times_times_int(sK27(X0,X1)),one_one_int) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_346]) ).

tcf(c_79086,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( number_number_of_int(sK27(X0,X1)) = sK27(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78002,c_254]) ).

tcf(c_79087,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_880]) ).

tcf(c_79088,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_608]) ).

tcf(c_79089,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_524]) ).

tcf(c_79090,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_523]) ).

tcf(c_79091,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_347]) ).

tcf(c_79092,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_346]) ).

tcf(c_79093,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X0,X1))
      | ( number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_254]) ).

tcf(c_79136,plain,
    ( is_int(hAPP_int_int(iPr_def_13,iPr_def_15))
    | ~ is_int(hAPP_int_int(iPr_def_13,iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_78938,c_65]) ).

tcf(c_79137,plain,
    ( is_int(hAPP_int_int(iPr_def_13,iPr_def_15))
    | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_78938,c_76880]) ).

tcf(c_79138,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_14196,c_59634,c_59635]) ).

tcf(c_79139,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),zero_zero_real))
    | ( zero_zero_nat = iPr_def_11 ) ),
    inference(superposition,[status(thm)],[c_495,c_79138]) ).

tcf(c_79141,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_nat_int(power_power_int(X0),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_14226,c_59634,c_59635]) ).

tcf(c_79143,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int)),
    inference(superposition,[status(thm)],[c_673,c_79141]) ).

tcf(c_79144,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_nat_int(power_power_int(X0),iPr_def_11),hAPP_i1948725293t_bool(ord_less_eq_int,X0))),
    inference(superposition,[status(thm)],[c_79141,c_226]) ).

tcf(c_79145,plain,
    ! [X0: $i] : is_int(sK27(X0,hAPP_nat_int(power_power_int(one_one_int),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79141,c_46404]) ).

tcf(c_79147,plain,
    ( ( number_number_of_int(hAPP_int_int(times_times_int(min),min)) = one_one_int )
    | ~ is_int(min) ),
    inference(light_normalisation,[status(thm)],[c_46426,c_76397]) ).

tcf(c_79148,plain,
    number_number_of_int(hAPP_int_int(times_times_int(min),min)) = one_one_int,
    inference(forward_subsumption_resolution,[status(thm)],[c_79147,c_56]) ).

tcf(c_79150,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(light_normalisation,[status(thm)],[c_371,c_59636,c_59638]) ).

tcf(c_79151,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)),
    inference(demodulation,[status(thm)],[c_78250,c_79150]) ).

tcf(c_79152,plain,
    hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = iPr_def_14,
    inference(demodulation,[status(thm)],[c_76924,c_79150]) ).

tcf(c_79154,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(demodulation,[status(thm)],[c_78434,c_79151]) ).

tcf(c_79161,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_79150,c_78930]) ).

tcf(c_79162,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_78625]) ).

tcf(c_79163,plain,
    ! [X0: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_79150,c_78442]) ).

tcf(c_79164,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_78126]) ).

tcf(c_79165,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),X0) != one_one_int,
    inference(superposition,[status(thm)],[c_79150,c_77377]) ).

tcf(c_79166,plain,
    ! [X0: $i] : is_int(number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_79150,c_77940]) ).

tcf(c_79167,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0))) = number267125858f_real(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_79150,c_77964]) ).

tcf(c_79168,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_12229]) ).

tcf(c_79169,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),X0) != iPr_def_15,
    inference(superposition,[status(thm)],[c_79150,c_76521]) ).

tcf(c_79170,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),X0) != min,
    inference(superposition,[status(thm)],[c_79150,c_755]) ).

tcf(c_79171,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(iPr_def_14),X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_79150,c_65]) ).

tcf(c_79173,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_14),X1)),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1))),X0),
    inference(superposition,[status(thm)],[c_79150,c_78759]) ).

tcf(c_79174,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X0)) != hAPP_int_int(times_times_int(iPr_def_14),X1),
    inference(superposition,[status(thm)],[c_79150,c_76515]) ).

tcf(c_79175,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_59645]) ).

tcf(c_79177,plain,
    ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_11305]) ).

tcf(c_79178,plain,
    hBOOL(member_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_79150,c_76545]) ).

tcf(c_79179,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_1135]) ).

tcf(c_79181,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_79150,c_1042]) ).

tcf(c_79182,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(X0),X0),hAPP_int_int(times_times_int(X1),X0)),X0)),
    inference(superposition,[status(thm)],[c_79150,c_833]) ).

tcf(c_79183,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X0),X0))
      | ~ is_int(iPr_def_14) ),
    inference(superposition,[status(thm)],[c_79150,c_76863]) ).

tcf(c_79184,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79150,c_253]) ).

tcf(c_79185,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_76535]) ).

tcf(c_79186,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_79150,c_76498]) ).

tcf(c_79187,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_79150,c_1045]) ).

tcf(c_79188,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(plus_plus_int(X1),X1)),X1)),
    inference(superposition,[status(thm)],[c_79150,c_833]) ).

tcf(c_79190,plain,
    hAPP_int_int(plus_plus_int(m),m) = hAPP_int_int(iPr_def_13,iPr_def_14),
    inference(superposition,[status(thm)],[c_79150,c_76855]) ).

tcf(c_79191,plain,
    ! [X0: $i] : is_int(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_79183,c_76346]) ).

tcf(c_79216,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_79191]) ).

tcf(c_79219,plain,
    is_int(hAPP_int_int(iPr_def_12,one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_79191]) ).

tcf(c_79220,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X0)),pls) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_880]) ).

tcf(c_79221,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_nat) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_608]) ).

tcf(c_79222,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),pls) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_524]) ).

tcf(c_79223,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_523]) ).

tcf(c_79224,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_347]) ).

tcf(c_79225,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_int) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_346]) ).

tcf(c_79226,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_79191,c_254]) ).

tcf(c_79239,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_253,c_79216]) ).

tcf(c_79242,plain,
    is_int(hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_76855,c_79216]) ).

tcf(c_79244,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),pls) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_880]) ).

tcf(c_79245,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_608]) ).

tcf(c_79246,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),pls) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_524]) ).

tcf(c_79247,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_14),X0)) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_523]) ).

tcf(c_79248,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_14),X0)) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_347]) ).

tcf(c_79249,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),one_one_int) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_346]) ).

tcf(c_79250,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0)) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_79216,c_254]) ).

tcf(c_79262,plain,
    is_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79150,c_79239]) ).

tcf(c_79264,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),pls) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_880]) ).

tcf(c_79265,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),one_one_nat) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_608]) ).

tcf(c_79266,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),pls) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_524]) ).

tcf(c_79267,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),iPr_def_14)) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_523]) ).

tcf(c_79268,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),iPr_def_14)) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_347]) ).

tcf(c_79269,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),one_one_int) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_346]) ).

tcf(c_79270,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_14)) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_254]) ).

tcf(c_79279,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(times_times_int(iPr_def_14),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_79175]) ).

tcf(c_79280,plain,
    hAPP_int_int(times_times_int(iPr_def_14),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_79175]) ).

tcf(c_79281,plain,
    hAPP_int_int(times_times_int(iPr_def_14),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_79279,c_78498]) ).

tcf(c_79285,plain,
    ! [X0: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))),
    inference(superposition,[status(thm)],[c_253,c_79163]) ).

tcf(c_79288,plain,
    is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(superposition,[status(thm)],[c_76855,c_79163]) ).

tcf(c_79290,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_880]) ).

tcf(c_79291,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),one_one_nat) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_608]) ).

tcf(c_79292,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_524]) ).

tcf(c_79293,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_523]) ).

tcf(c_79294,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_347]) ).

tcf(c_79295,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),one_one_int) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_346]) ).

tcf(c_79296,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79163,c_254]) ).

tcf(c_79305,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_880]) ).

tcf(c_79306,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),one_one_nat) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_608]) ).

tcf(c_79307,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_524]) ).

tcf(c_79308,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_523]) ).

tcf(c_79309,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_347]) ).

tcf(c_79310,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),one_one_int) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_346]) ).

tcf(c_79311,plain,
    number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_254]) ).

tcf(c_79312,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),iPr_def_14) != one_one_int,
    inference(superposition,[status(thm)],[c_253,c_79165]) ).

tcf(c_79315,plain,
    hAPP_int_int(iPr_def_13,iPr_def_14) != one_one_int,
    inference(superposition,[status(thm)],[c_76855,c_79165]) ).

tcf(c_79318,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_78939,c_79151]) ).

tcf(c_79319,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(demodulation,[status(thm)],[c_79318,c_79161]) ).

tcf(c_79320,plain,
    hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(pls),pls))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),min))),
    inference(superposition,[status(thm)],[c_77407,c_79319]) ).

tcf(c_79321,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_79150,c_79319]) ).

tcf(c_79322,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ is_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))) ),
    inference(superposition,[status(thm)],[c_79319,c_65]) ).

tcf(c_79323,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_79319,c_77366]) ).

tcf(c_79324,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_77054]) ).

tcf(c_79325,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_79319,c_76606]) ).

tcf(c_79326,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))))),
    inference(superposition,[status(thm)],[c_79319,c_76597]) ).

tcf(c_79327,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_76534]) ).

tcf(c_79328,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_76497]) ).

tcf(c_79329,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))))
      | ~ is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_79319,c_65]) ).

tcf(c_79330,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_77366]) ).

tcf(c_79331,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_77054]) ).

tcf(c_79332,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),hAPP_i1948725293t_bool(dvd_dvd_int,m))),
    inference(superposition,[status(thm)],[c_79319,c_76606]) ).

tcf(c_79333,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_76597]) ).

tcf(c_79334,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))))),
    inference(superposition,[status(thm)],[c_79319,c_76534]) ).

tcf(c_79335,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))))),
    inference(superposition,[status(thm)],[c_79319,c_76497]) ).

tcf(c_79336,plain,
    hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),min))) = hAPP_int_int(iPr_def_13,min),
    inference(light_normalisation,[status(thm)],[c_79320,c_340,c_77407]) ).

tcf(c_79342,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),X0) = hAPP_nat_nat(times_times_nat(iPr_def_11),X0),
    inference(light_normalisation,[status(thm)],[c_372,c_59634,c_59635]) ).

tcf(c_79347,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(iPr_def_11),X0) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_79342,c_1324]) ).

tcf(c_79349,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(iPr_def_11),X0) != X0 ) ),
    inference(superposition,[status(thm)],[c_79342,c_1321]) ).

tcf(c_79351,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X0)),
    inference(superposition,[status(thm)],[c_79342,c_1344]) ).

tcf(c_79353,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_79342,c_1327]) ).

tcf(c_79354,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X0) = X0,
    inference(superposition,[status(thm)],[c_79342,c_1290]) ).

tcf(c_79357,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X0))),
    inference(superposition,[status(thm)],[c_79342,c_1375]) ).

tcf(c_79359,plain,
    hAPP_nat_nat(times_times_nat(iPr_def_11),one_one_nat) = hAPP_nat_nat(iPr_def_10,one_one_nat),
    inference(superposition,[status(thm)],[c_79342,c_77521]) ).

tcf(c_79360,plain,
    hAPP_nat_nat(times_times_nat(iPr_def_11),zero_zero_nat) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_79342,c_1326]) ).

tcf(c_79362,plain,
    hAPP_nat_nat(times_times_nat(iPr_def_11),one_one_nat) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_79359,c_59635]) ).

tcf(c_79378,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(plus_plus_real(X0),X0))),
    inference(superposition,[status(thm)],[c_373,c_1043]) ).

tcf(c_79380,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X0),X0))),
    inference(superposition,[status(thm)],[c_373,c_1040]) ).

tcf(c_79381,plain,
    hAPP_real_real(plus_plus_real(zero_zero_real),zero_zero_real) = zero_zero_real,
    inference(superposition,[status(thm)],[c_373,c_999]) ).

tcf(c_79382,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0) != X0 ) ),
    inference(superposition,[status(thm)],[c_373,c_517]) ).

tcf(c_79383,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_373,c_521]) ).

tcf(c_79394,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(pls),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(pls),X0)),
    inference(superposition,[status(thm)],[c_574,c_382]) ).

tcf(c_79395,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(min),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(min),X0)),
    inference(superposition,[status(thm)],[c_76397,c_382]) ).

tcf(c_79396,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(min),min)),X0)) = hAPP_int_int(times_times_int(one_one_int),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_79148,c_382]) ).

tcf(c_79397,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_76393,c_382]) ).

tcf(c_79398,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(undefined_int(int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(undefined_int(int)),X0)),
    inference(superposition,[status(thm)],[c_76395,c_382]) ).

tcf(c_79399,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),X1)),
    inference(superposition,[status(thm)],[c_76399,c_382]) ).

tcf(c_79400,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),X2)),
    inference(superposition,[status(thm)],[c_76401,c_382]) ).

tcf(c_79401,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(m),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(m),X0)),
    inference(superposition,[status(thm)],[c_76402,c_382]) ).

tcf(c_79402,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s1),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(s1),X0)),
    inference(superposition,[status(thm)],[c_76403,c_382]) ).

tcf(c_79403,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(s),X0)),
    inference(superposition,[status(thm)],[c_76404,c_382]) ).

tcf(c_79404,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(t),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(t),X0)),
    inference(superposition,[status(thm)],[c_76405,c_382]) ).

tcf(c_79405,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK9),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK9),X0)),
    inference(superposition,[status(thm)],[c_76406,c_382]) ).

tcf(c_79406,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK10),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK10),X0)),
    inference(superposition,[status(thm)],[c_76407,c_382]) ).

tcf(c_79407,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK11),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK11),X0)),
    inference(superposition,[status(thm)],[c_76408,c_382]) ).

tcf(c_79408,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK13),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK13),X0)),
    inference(superposition,[status(thm)],[c_76409,c_382]) ).

tcf(c_79409,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_76410,c_382]) ).

tcf(c_79410,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_15),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),X0)),
    inference(superposition,[status(thm)],[c_76411,c_382]) ).

tcf(c_79411,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_16),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),X0)),
    inference(superposition,[status(thm)],[c_76412,c_382]) ).

tcf(c_79412,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_17),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_17),X0)),
    inference(superposition,[status(thm)],[c_76413,c_382]) ).

tcf(c_79413,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_18),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),X0)),
    inference(superposition,[status(thm)],[c_76414,c_382]) ).

tcf(c_79414,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_76415,c_382]) ).

tcf(c_79415,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),X1)),
    inference(superposition,[status(thm)],[c_77366,c_382]) ).

tcf(c_79416,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK26(iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),X0)),
    inference(superposition,[status(thm)],[c_78203,c_382]) ).

tcf(c_79417,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),pls) = number_number_of_int(hAPP_int_int(times_times_int(X0),pls)),
    inference(superposition,[status(thm)],[c_574,c_382]) ).

tcf(c_79418,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),min) = number_number_of_int(hAPP_int_int(times_times_int(X0),min)),
    inference(superposition,[status(thm)],[c_76397,c_382]) ).

tcf(c_79419,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(min),min))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),one_one_int),
    inference(superposition,[status(thm)],[c_79148,c_382]) ).

tcf(c_79420,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(times_times_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_382]) ).

tcf(c_79421,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),undefined_int(int)) = number_number_of_int(hAPP_int_int(times_times_int(X0),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_382]) ).

tcf(c_79422,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),twoSqu1241645765sum2sq(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_382]) ).

tcf(c_79423,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(X1,X2)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_382]) ).

tcf(c_79424,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),m) = number_number_of_int(hAPP_int_int(times_times_int(X0),m)),
    inference(superposition,[status(thm)],[c_76402,c_382]) ).

tcf(c_79425,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),s1) = number_number_of_int(hAPP_int_int(times_times_int(X0),s1)),
    inference(superposition,[status(thm)],[c_76403,c_382]) ).

tcf(c_79426,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),s) = number_number_of_int(hAPP_int_int(times_times_int(X0),s)),
    inference(superposition,[status(thm)],[c_76404,c_382]) ).

tcf(c_79427,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),t) = number_number_of_int(hAPP_int_int(times_times_int(X0),t)),
    inference(superposition,[status(thm)],[c_76405,c_382]) ).

tcf(c_79428,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK9) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_382]) ).

tcf(c_79429,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK10) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_382]) ).

tcf(c_79430,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK11) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_382]) ).

tcf(c_79431,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK13) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_382]) ).

tcf(c_79432,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_14) = number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_382]) ).

tcf(c_79433,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_15) = number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_382]) ).

tcf(c_79434,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_16) = number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_382]) ).

tcf(c_79435,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_17) = number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_382]) ).

tcf(c_79436,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_18) = number_number_of_int(hAPP_int_int(times_times_int(X0),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_382]) ).

tcf(c_79437,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_382]) ).

tcf(c_79438,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_382]) ).

tcf(c_79439,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK26(iPr_def_14)) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_382]) ).

tcf(c_79440,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X1),X0)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_382,c_65]) ).

tcf(c_79441,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_382,c_11305]) ).

tcf(c_79442,plain,
    ! [X0: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_382,c_76545]) ).

tcf(c_79443,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_382,c_1135]) ).

tcf(c_79445,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(X1),X0)))),
    inference(superposition,[status(thm)],[c_382,c_1042]) ).

tcf(c_79446,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),number_number_of_int(X1))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_382,c_833]) ).

tcf(c_79447,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_382,c_76863]) ).

tcf(c_79448,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X1),X0)),
    inference(superposition,[status(thm)],[c_382,c_253]) ).

tcf(c_79449,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_382,c_76535]) ).

tcf(c_79450,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_382,c_76498]) ).

tcf(c_79451,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_382,c_1045]) ).

tcf(c_79452,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(X1)),number_number_of_int(hAPP_int_int(times_times_int(X2),X1))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_382,c_833]) ).

tcf(c_79457,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),iPr_def_14) = hAPP_int_int(times_times_int(X0),iPr_def_14),
    inference(light_normalisation,[status(thm)],[c_79432,c_79270]) ).

tcf(c_79458,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),m) = hAPP_int_int(iPr_def_13,X0),
    inference(light_normalisation,[status(thm)],[c_79424,c_76855,c_77366]) ).

tcf(c_79459,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),pls) = pls,
    inference(light_normalisation,[status(thm)],[c_79417,c_1001,c_574]) ).

tcf(c_79460,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),number_number_of_int(X0)) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(light_normalisation,[status(thm)],[c_79409,c_79250]) ).

tcf(c_79461,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,number_number_of_int(X0)) = hAPP_int_int(iPr_def_13,X0),
    inference(light_normalisation,[status(thm)],[c_79401,c_59637,c_77366]) ).

tcf(c_79462,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(pls),number_number_of_int(X0)) = pls,
    inference(light_normalisation,[status(thm)],[c_79394,c_1004,c_574]) ).

tcf(c_79463,plain,
    hAPP_int_int(times_times_int(min),number_number_of_int(min)) = one_one_int,
    inference(demodulation,[status(thm)],[c_79148,c_79395]) ).

tcf(c_79464,plain,
    hAPP_int_int(times_times_int(min),min) = one_one_int,
    inference(light_normalisation,[status(thm)],[c_79463,c_76397]) ).

tcf(c_79519,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(zero_zero_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(times_times_int(pls),X0)),
    inference(superposition,[status(thm)],[c_568,c_383]) ).

tcf(c_79520,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(times_times_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_78124,c_383]) ).

tcf(c_79521,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),zero_zero_real) = number267125858f_real(hAPP_int_int(times_times_int(X0),pls)),
    inference(superposition,[status(thm)],[c_568,c_383]) ).

tcf(c_79522,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(times_times_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_78124,c_383]) ).

tcf(c_79523,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(X0),X0))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_383,c_1201]) ).

tcf(c_79524,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_383,c_1134]) ).

tcf(c_79526,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X0)),number267125858f_real(hAPP_int_int(times_times_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_383,c_1043]) ).

tcf(c_79527,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(times_times_int(X1),X0)),
    inference(superposition,[status(thm)],[c_383,c_976]) ).

tcf(c_79528,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X0)),number267125858f_real(hAPP_int_int(times_times_int(X1),X0)))),
    inference(superposition,[status(thm)],[c_383,c_1040]) ).

tcf(c_79529,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),zero_zero_real) = zero_zero_real,
    inference(light_normalisation,[status(thm)],[c_79521,c_1001,c_568]) ).

tcf(c_79530,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(zero_zero_real),number267125858f_real(X0)) = zero_zero_real,
    inference(light_normalisation,[status(thm)],[c_79519,c_1004,c_568]) ).

tcf(c_79541,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(one_one_int,hAPP_int_int(times_times_int(X0),min)),min)),
    inference(superposition,[status(thm)],[c_79464,c_833]) ).

tcf(c_79543,plain,
    hBOOL(member_int(one_one_int,hAPP_i1948725293t_bool(dvd_dvd_int,min))),
    inference(superposition,[status(thm)],[c_79464,c_76535]) ).

tcf(c_79545,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),one_one_int)),
    inference(superposition,[status(thm)],[c_79464,c_1045]) ).

tcf(c_79546,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),min),one_one_int),min)),
    inference(superposition,[status(thm)],[c_79464,c_833]) ).

tcf(c_79551,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),iPr_def_14) != iPr_def_15,
    inference(superposition,[status(thm)],[c_253,c_79169]) ).

tcf(c_79554,plain,
    hAPP_int_int(iPr_def_13,iPr_def_14) != iPr_def_15,
    inference(superposition,[status(thm)],[c_76855,c_79169]) ).

tcf(c_79557,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_253,c_79414]) ).

tcf(c_79559,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_1001,c_79414]) ).

tcf(c_79560,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(m)) = number_number_of_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76855,c_79414]) ).

tcf(c_79561,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79414,c_382]) ).

tcf(c_79562,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79414,c_58]) ).

tcf(c_79563,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79414,c_382]) ).

tcf(c_79564,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls) = pls,
    inference(light_normalisation,[status(thm)],[c_79559,c_574]) ).

tcf(c_79565,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) = number_number_of_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_79560,c_76402]) ).

tcf(c_79573,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_253,c_79437]) ).

tcf(c_79575,plain,
    hAPP_int_int(times_times_int(number_number_of_int(pls)),sK30(iPr_def_19)) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_1004,c_79437]) ).

tcf(c_79576,plain,
    hAPP_int_int(times_times_int(number_number_of_int(one_one_int)),sK30(iPr_def_19)) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_76995,c_79437]) ).

tcf(c_79577,plain,
    hAPP_int_int(times_times_int(number_number_of_int(m)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59637,c_79437]) ).

tcf(c_79578,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79437,c_382]) ).

tcf(c_79579,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79437,c_58]) ).

tcf(c_79580,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_382]) ).

tcf(c_79581,plain,
    hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_79414]) ).

tcf(c_79582,plain,
    hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)) = pls,
    inference(light_normalisation,[status(thm)],[c_79575,c_574]) ).

tcf(c_79584,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) = hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_79577,c_59637,c_76402,c_79565]) ).

tcf(c_79596,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(one_one_int)) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_76995,c_79557]) ).

tcf(c_79598,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79557,c_382]) ).

tcf(c_79599,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79557,c_58]) ).

tcf(c_79600,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79557,c_382]) ).

tcf(c_79601,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_79557,c_79437]) ).

tcf(c_79612,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_253,c_79562]) ).

tcf(c_79636,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79414,c_79562]) ).

tcf(c_79637,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79557,c_79562]) ).

tcf(c_79638,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_79562]) ).

tcf(c_79639,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_880]) ).

tcf(c_79640,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_608]) ).

tcf(c_79641,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_524]) ).

tcf(c_79642,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_523]) ).

tcf(c_79643,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_347]) ).

tcf(c_79644,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_346]) ).

tcf(c_79645,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_254]) ).

tcf(c_79685,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79573,c_79562]) ).

tcf(c_79686,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79573,c_382]) ).

tcf(c_79688,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_382]) ).

tcf(c_79724,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79573,c_79579]) ).

tcf(c_79725,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79414,c_79579]) ).

tcf(c_79726,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79557,c_79579]) ).

tcf(c_79727,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79437,c_79579]) ).

tcf(c_79728,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_880]) ).

tcf(c_79729,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_608]) ).

tcf(c_79730,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_524]) ).

tcf(c_79731,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_523]) ).

tcf(c_79732,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_347]) ).

tcf(c_79733,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_346]) ).

tcf(c_79734,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_254]) ).

tcf(c_79768,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),X0))),
    inference(demodulation,[status(thm)],[c_79561,c_252,c_253,c_79448,c_79573]) ).

tcf(c_79771,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_574,c_79563]) ).

tcf(c_79772,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76397,c_79563]) ).

tcf(c_79773,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76393,c_79563]) ).

tcf(c_79774,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76395,c_79563]) ).

tcf(c_79775,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_76399,c_79563]) ).

tcf(c_79776,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X2))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2))),
    inference(superposition,[status(thm)],[c_76401,c_79563]) ).

tcf(c_79777,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76402,c_79563]) ).

tcf(c_79778,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76403,c_79563]) ).

tcf(c_79779,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76404,c_79563]) ).

tcf(c_79780,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76405,c_79563]) ).

tcf(c_79781,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76406,c_79563]) ).

tcf(c_79782,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76407,c_79563]) ).

tcf(c_79783,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76408,c_79563]) ).

tcf(c_79784,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76409,c_79563]) ).

tcf(c_79785,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76410,c_79563]) ).

tcf(c_79786,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76411,c_79563]) ).

tcf(c_79787,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76412,c_79563]) ).

tcf(c_79788,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76413,c_79563]) ).

tcf(c_79789,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76414,c_79563]) ).

tcf(c_79790,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_76415,c_79563]) ).

tcf(c_79791,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_77366,c_79563]) ).

tcf(c_79792,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_78203,c_79563]) ).

tcf(c_79793,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_79563]) ).

tcf(c_79794,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79414,c_79563]) ).

tcf(c_79795,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79557,c_79563]) ).

tcf(c_79796,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79437,c_79563]) ).

tcf(c_79799,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),
    inference(superposition,[status(thm)],[c_574,c_79563]) ).

tcf(c_79800,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))),
    inference(superposition,[status(thm)],[c_76397,c_79563]) ).

tcf(c_79801,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_79563]) ).

tcf(c_79802,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_79563]) ).

tcf(c_79803,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X1)))),
    inference(superposition,[status(thm)],[c_76399,c_79563]) ).

tcf(c_79804,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X1,X2))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X1,X2)))),
    inference(superposition,[status(thm)],[c_76401,c_79563]) ).

tcf(c_79805,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))),
    inference(superposition,[status(thm)],[c_76402,c_79563]) ).

tcf(c_79806,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))),
    inference(superposition,[status(thm)],[c_76403,c_79563]) ).

tcf(c_79807,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))),
    inference(superposition,[status(thm)],[c_76404,c_79563]) ).

tcf(c_79808,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))),
    inference(superposition,[status(thm)],[c_76405,c_79563]) ).

tcf(c_79809,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_79563]) ).

tcf(c_79810,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_79563]) ).

tcf(c_79811,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_79563]) ).

tcf(c_79812,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_79563]) ).

tcf(c_79813,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_79563]) ).

tcf(c_79814,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_79563]) ).

tcf(c_79815,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_79563]) ).

tcf(c_79816,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_79563]) ).

tcf(c_79817,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_79563]) ).

tcf(c_79818,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76415,c_79563]) ).

tcf(c_79819,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X1)))),
    inference(superposition,[status(thm)],[c_77366,c_79563]) ).

tcf(c_79820,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_79563]) ).

tcf(c_79821,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79573,c_79563]) ).

tcf(c_79822,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79414,c_79563]) ).

tcf(c_79823,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79557,c_79563]) ).

tcf(c_79824,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_79563]) ).

tcf(c_79825,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_79563,c_65]) ).

tcf(c_79827,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))))),
    inference(superposition,[status(thm)],[c_79563,c_1042]) ).

tcf(c_79828,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79563,c_833]) ).

tcf(c_79829,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_79563,c_76863]) ).

tcf(c_79830,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_79563,c_253]) ).

tcf(c_79831,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79563,c_76535]) ).

tcf(c_79832,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_79563,c_76498]) ).

tcf(c_79833,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_79563,c_1045]) ).

tcf(c_79834,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79563,c_833]) ).

tcf(c_79839,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(light_normalisation,[status(thm)],[c_79777,c_59637]) ).

tcf(c_79901,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))),
    inference(superposition,[status(thm)],[c_253,c_79161]) ).

tcf(c_79904,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(superposition,[status(thm)],[c_76855,c_79161]) ).

tcf(c_79906,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))
      | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(superposition,[status(thm)],[c_79161,c_65]) ).

tcf(c_79907,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))
      | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_79161,c_76880]) ).

tcf(c_79912,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(pls),X0)),
    inference(superposition,[status(thm)],[c_574,c_388]) ).

tcf(c_79913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(min),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(min),X0)),
    inference(superposition,[status(thm)],[c_76397,c_388]) ).

tcf(c_79914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_76393,c_388]) ).

tcf(c_79915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(undefined_int(int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(undefined_int(int)),X0)),
    inference(superposition,[status(thm)],[c_76395,c_388]) ).

tcf(c_79916,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),X1)),
    inference(superposition,[status(thm)],[c_76399,c_388]) ).

tcf(c_79917,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(X0,X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(X0,X1)),X2)),
    inference(superposition,[status(thm)],[c_76401,c_388]) ).

tcf(c_79918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)),
    inference(superposition,[status(thm)],[c_76402,c_388]) ).

tcf(c_79919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(s1),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(s1),X0)),
    inference(superposition,[status(thm)],[c_76403,c_388]) ).

tcf(c_79920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(s),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(s),X0)),
    inference(superposition,[status(thm)],[c_76404,c_388]) ).

tcf(c_79921,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(t),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(t),X0)),
    inference(superposition,[status(thm)],[c_76405,c_388]) ).

tcf(c_79922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK9),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK9),X0)),
    inference(superposition,[status(thm)],[c_76406,c_388]) ).

tcf(c_79923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK10),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK10),X0)),
    inference(superposition,[status(thm)],[c_76407,c_388]) ).

tcf(c_79924,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK11),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK11),X0)),
    inference(superposition,[status(thm)],[c_76408,c_388]) ).

tcf(c_79925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK13),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK13),X0)),
    inference(superposition,[status(thm)],[c_76409,c_388]) ).

tcf(c_79926,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_76410,c_388]) ).

tcf(c_79927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_15),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(iPr_def_15),X0)),
    inference(superposition,[status(thm)],[c_76411,c_388]) ).

tcf(c_79928,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_16),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(iPr_def_16),X0)),
    inference(superposition,[status(thm)],[c_76412,c_388]) ).

tcf(c_79929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_17),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(iPr_def_17),X0)),
    inference(superposition,[status(thm)],[c_76413,c_388]) ).

tcf(c_79930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_18),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(iPr_def_18),X0)),
    inference(superposition,[status(thm)],[c_76414,c_388]) ).

tcf(c_79931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_76415,c_388]) ).

tcf(c_79932,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),X1)),
    inference(superposition,[status(thm)],[c_77366,c_388]) ).

tcf(c_79933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),X0)),
    inference(superposition,[status(thm)],[c_78203,c_388]) ).

tcf(c_79934,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79573,c_388]) ).

tcf(c_79935,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79414,c_388]) ).

tcf(c_79936,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79557,c_388]) ).

tcf(c_79937,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79437,c_388]) ).

tcf(c_79938,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),pls) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),pls)),
    inference(superposition,[status(thm)],[c_574,c_388]) ).

tcf(c_79939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),min) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),min)),
    inference(superposition,[status(thm)],[c_76397,c_388]) ).

tcf(c_79940,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_388]) ).

tcf(c_79941,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),undefined_int(int)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_388]) ).

tcf(c_79942,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),twoSqu1241645765sum2sq(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_388]) ).

tcf(c_79943,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_nat_int(X1,X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_388]) ).

tcf(c_79944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),m) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)),
    inference(superposition,[status(thm)],[c_76402,c_388]) ).

tcf(c_79945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),s1) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),s1)),
    inference(superposition,[status(thm)],[c_76403,c_388]) ).

tcf(c_79946,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),s) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),s)),
    inference(superposition,[status(thm)],[c_76404,c_388]) ).

tcf(c_79947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),t) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),t)),
    inference(superposition,[status(thm)],[c_76405,c_388]) ).

tcf(c_79948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK9) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_388]) ).

tcf(c_79949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK10) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_388]) ).

tcf(c_79950,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK11) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_388]) ).

tcf(c_79951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK13) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_388]) ).

tcf(c_79952,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),iPr_def_14) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_388]) ).

tcf(c_79953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),iPr_def_15) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_388]) ).

tcf(c_79954,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),iPr_def_16) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_388]) ).

tcf(c_79955,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),iPr_def_17) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_388]) ).

tcf(c_79956,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),iPr_def_18) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_388]) ).

tcf(c_79957,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_388]) ).

tcf(c_79958,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_388]) ).

tcf(c_79959,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK26(iPr_def_14)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_388]) ).

tcf(c_79960,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_388]) ).

tcf(c_79961,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79414,c_388]) ).

tcf(c_79962,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79557,c_388]) ).

tcf(c_79963,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_388]) ).

tcf(c_79964,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),number_number_of_int(X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_388,c_79319]) ).

tcf(c_79966,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(times_times_int(iPr_def_14),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_388,c_79150]) ).

tcf(c_79967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_388,c_78930]) ).

tcf(c_79968,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) = hAPP_int_int(minus_minus_int(min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_388,c_78625]) ).

tcf(c_79969,plain,
    ! [X0: $i] : is_int(hAPP_int_int(minus_minus_int(min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_388,c_78442]) ).

tcf(c_79970,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) != one_one_int,
    inference(superposition,[status(thm)],[c_388,c_77377]) ).

tcf(c_79971,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) = number267125858f_real(hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_388,c_77964]) ).

tcf(c_79972,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) != iPr_def_15,
    inference(superposition,[status(thm)],[c_388,c_76521]) ).

tcf(c_79973,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) != min,
    inference(superposition,[status(thm)],[c_388,c_755]) ).

tcf(c_79974,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),X0)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_388,c_65]) ).

tcf(c_79975,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_388,c_76880]) ).

tcf(c_79977,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)))),X0),
    inference(superposition,[status(thm)],[c_388,c_78759]) ).

tcf(c_79978,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X0)) != number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_388,c_76515]) ).

tcf(c_79979,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X0)),
    inference(superposition,[status(thm)],[c_388,c_257]) ).

tcf(c_79988,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(times_times_int(iPr_def_14),X0),
    inference(light_normalisation,[status(thm)],[c_79966,c_79226,c_79460]) ).

tcf(c_79989,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),one_one_int) = hAPP_int_int(iPr_def_12,X0),
    inference(light_normalisation,[status(thm)],[c_79940,c_76874,c_78024]) ).

tcf(c_79990,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(X0)) = hAPP_int_int(iPr_def_12,X0),
    inference(light_normalisation,[status(thm)],[c_79914,c_59636,c_78024]) ).

tcf(c_79994,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),number_number_of_int(X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),
    inference(light_normalisation,[status(thm)],[c_79964,c_79226]) ).

tcf(c_80118,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(pls),X0)),
    inference(superposition,[status(thm)],[c_568,c_389]) ).

tcf(c_80119,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_78124,c_389]) ).

tcf(c_80120,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),zero_zero_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),pls)),
    inference(superposition,[status(thm)],[c_568,c_389]) ).

tcf(c_80121,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_78124,c_389]) ).

tcf(c_80122,plain,
    ! [X0: $i,X1: $i] :
      ( ( number267125858f_real(X1) = zero_zero_real )
      | ( number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1)) != number267125858f_real(X0) ) ),
    inference(superposition,[status(thm)],[c_389,c_517]) ).

tcf(c_80123,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X0)),
    inference(superposition,[status(thm)],[c_389,c_243]) ).

tcf(c_80126,plain,
    ! [X0: $i] :
      ( ( number267125858f_real(X0) = zero_zero_real )
      | ( number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_389,c_521]) ).

tcf(c_80127,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(iPr_def_12,X0)),
    inference(light_normalisation,[status(thm)],[c_80121,c_76874]) ).

tcf(c_80128,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(iPr_def_12,X0)),
    inference(light_normalisation,[status(thm)],[c_80119,c_59636]) ).

tcf(c_80133,plain,
    number267125858f_real(hAPP_int_int(iPr_def_12,iPr_def_14)) = number267125858f_real(iPr_def_15),
    inference(demodulation,[status(thm)],[c_77968,c_80128]) ).

tcf(c_80146,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_12,pls)))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_78137,c_611]) ).

tcf(c_80147,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int))
    | ~ is_int(pls) ),
    inference(light_normalisation,[status(thm)],[c_80146,c_77245]) ).

tcf(c_80152,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)),
    inference(superposition,[status(thm)],[c_74,c_612]) ).

tcf(c_80154,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1563,c_612]) ).

tcf(c_80155,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_46418,c_612]) ).

tcf(c_80156,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(one_one_int),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79141,c_612]) ).

tcf(c_80162,plain,
    hBOOL(member_int(t,hAPP_i1948725293t_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_80152,c_226]) ).

tcf(c_80165,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),iPr_def_14) != min,
    inference(superposition,[status(thm)],[c_253,c_79170]) ).

tcf(c_80168,plain,
    hAPP_int_int(iPr_def_13,iPr_def_14) != min,
    inference(superposition,[status(thm)],[c_76855,c_79170]) ).

tcf(c_80177,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79150,c_79931]) ).

tcf(c_80178,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_257,c_79931]) ).

tcf(c_80180,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(one_one_int)) = number_number_of_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76874,c_79931]) ).

tcf(c_80181,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78759,c_79931]) ).

tcf(c_80182,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79931,c_388]) ).

tcf(c_80183,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79931,c_79563]) ).

tcf(c_80184,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79931,c_79579]) ).

tcf(c_80185,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79931,c_79562]) ).

tcf(c_80186,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79931,c_382]) ).

tcf(c_80187,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79931,c_58]) ).

tcf(c_80188,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79931,c_388]) ).

tcf(c_80189,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79931,c_79563]) ).

tcf(c_80190,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79931,c_382]) ).

tcf(c_80191,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),one_one_int) = number_number_of_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_80180,c_76393]) ).

tcf(c_80194,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_80177,c_76415]) ).

tcf(c_80218,plain,
    hAPP_int_int(plus_plus_int(number_number_of_int(sK30(iPr_def_19))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79150,c_79957]) ).

tcf(c_80219,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_257,c_79957]) ).

tcf(c_80221,plain,
    hAPP_int_int(plus_plus_int(number_number_of_int(pls)),sK30(iPr_def_19)) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_77165,c_79957]) ).

tcf(c_80222,plain,
    hAPP_int_int(plus_plus_int(number_number_of_int(one_one_int)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59636,c_79957]) ).

tcf(c_80223,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79957,c_388]) ).

tcf(c_80224,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79957,c_79563]) ).

tcf(c_80225,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79957,c_79579]) ).

tcf(c_80226,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_79562]) ).

tcf(c_80227,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79957,c_382]) ).

tcf(c_80228,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79957,c_58]) ).

tcf(c_80229,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_388]) ).

tcf(c_80230,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79957,c_79563]) ).

tcf(c_80231,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_382]) ).

tcf(c_80232,plain,
    hAPP_int_int(plus_plus_int(number_number_of_int(sK30(iPr_def_19))),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_79931]) ).

tcf(c_80234,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),one_one_int) = hAPP_int_int(iPr_def_12,sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_80222,c_59636,c_76393,c_80191]) ).

tcf(c_80257,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_79790,c_253,c_79573]) ).

tcf(c_80258,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_80257]) ).

tcf(c_80259,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_76399,c_80257]) ).

tcf(c_80260,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_76401,c_80257]) ).

tcf(c_80261,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_77366,c_80257]) ).

tcf(c_80262,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_80257]) ).

tcf(c_80264,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_80257]) ).

tcf(c_80266,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_80257]) ).

tcf(c_80267,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79931,c_80257]) ).

tcf(c_80268,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_80257]) ).

tcf(c_80269,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_574,c_80257]) ).

tcf(c_80270,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76397,c_80257]) ).

tcf(c_80271,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_80257]) ).

tcf(c_80272,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_80257]) ).

tcf(c_80273,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76403,c_80257]) ).

tcf(c_80274,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76404,c_80257]) ).

tcf(c_80275,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76405,c_80257]) ).

tcf(c_80276,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76406,c_80257]) ).

tcf(c_80277,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76407,c_80257]) ).

tcf(c_80278,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76408,c_80257]) ).

tcf(c_80279,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76409,c_80257]) ).

tcf(c_80280,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76410,c_80257]) ).

tcf(c_80281,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76411,c_80257]) ).

tcf(c_80282,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76412,c_80257]) ).

tcf(c_80283,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76413,c_80257]) ).

tcf(c_80284,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76414,c_80257]) ).

tcf(c_80286,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80257,c_1042]) ).

tcf(c_80287,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_833]) ).

tcf(c_80288,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_80257,c_76863]) ).

tcf(c_80289,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_76535]) ).

tcf(c_80290,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80257,c_76498]) ).

tcf(c_80291,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80257,c_1045]) ).

tcf(c_80292,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_833]) ).

tcf(c_80293,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80257,c_79573]) ).

tcf(c_80294,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80257,c_79414]) ).

tcf(c_80295,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_78432]) ).

tcf(c_80296,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80257,c_78420]) ).

tcf(c_80297,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80257,c_78405]) ).

tcf(c_80298,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80257,c_78397]) ).

tcf(c_80300,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80257,c_1042]) ).

tcf(c_80301,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80257,c_833]) ).

tcf(c_80302,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_80257,c_76863]) ).

tcf(c_80303,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_76535]) ).

tcf(c_80304,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80257,c_76498]) ).

tcf(c_80305,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80257,c_1045]) ).

tcf(c_80306,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_80257,c_833]) ).

tcf(c_80307,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_79573]) ).

tcf(c_80308,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_79414]) ).

tcf(c_80309,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_78432]) ).

tcf(c_80310,plain,
    ! [X0: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80257,c_78420]) ).

tcf(c_80311,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80257,c_78405]) ).

tcf(c_80312,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80257,c_78397]) ).

tcf(c_80313,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_80302,c_76385]) ).

tcf(c_80314,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_80288,c_76385]) ).

tcf(c_80315,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_80272,c_59637]) ).

tcf(c_80316,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_80271,c_76995]) ).

tcf(c_80396,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_574,c_80313]) ).

tcf(c_80397,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76397,c_80313]) ).

tcf(c_80398,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76393,c_80313]) ).

tcf(c_80399,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76395,c_80313]) ).

tcf(c_80400,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76399,c_80313]) ).

tcf(c_80401,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76401,c_80313]) ).

tcf(c_80402,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76402,c_80313]) ).

tcf(c_80403,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76403,c_80313]) ).

tcf(c_80404,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76404,c_80313]) ).

tcf(c_80405,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76405,c_80313]) ).

tcf(c_80406,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76406,c_80313]) ).

tcf(c_80407,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76407,c_80313]) ).

tcf(c_80408,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76408,c_80313]) ).

tcf(c_80409,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76409,c_80313]) ).

tcf(c_80410,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76410,c_80313]) ).

tcf(c_80411,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76411,c_80313]) ).

tcf(c_80412,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76412,c_80313]) ).

tcf(c_80413,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76413,c_80313]) ).

tcf(c_80414,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76414,c_80313]) ).

tcf(c_80415,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76415,c_80313]) ).

tcf(c_80416,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_77366,c_80313]) ).

tcf(c_80417,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_78203,c_80313]) ).

tcf(c_80419,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79414,c_80313]) ).

tcf(c_80421,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_80313]) ).

tcf(c_80422,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79931,c_80313]) ).

tcf(c_80423,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_80313]) ).

tcf(c_80424,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_880]) ).

tcf(c_80425,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_608]) ).

tcf(c_80426,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_524]) ).

tcf(c_80427,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_523]) ).

tcf(c_80428,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_347]) ).

tcf(c_80429,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_346]) ).

tcf(c_80430,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_254]) ).

tcf(c_80431,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_80402,c_59637]) ).

tcf(c_80432,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_80398,c_76995]) ).

tcf(c_80433,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),
    inference(light_normalisation,[status(thm)],[c_80417,c_80262]) ).

tcf(c_80434,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),
    inference(light_normalisation,[status(thm)],[c_80399,c_80258]) ).

tcf(c_80435,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))),
    inference(light_normalisation,[status(thm)],[c_80416,c_80261]) ).

tcf(c_80436,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))),
    inference(light_normalisation,[status(thm)],[c_80401,c_80260]) ).

tcf(c_80437,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_80423,c_80268]) ).

tcf(c_80438,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(light_normalisation,[status(thm)],[c_80422,c_80267]) ).

tcf(c_80439,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_80421,c_80266]) ).

tcf(c_80440,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(light_normalisation,[status(thm)],[c_80419,c_80264]) ).

tcf(c_80499,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),
    inference(superposition,[status(thm)],[c_574,c_80314]) ).

tcf(c_80500,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))),
    inference(superposition,[status(thm)],[c_76397,c_80314]) ).

tcf(c_80501,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_80314]) ).

tcf(c_80503,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))),
    inference(superposition,[status(thm)],[c_76399,c_80314]) ).

tcf(c_80505,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))),
    inference(superposition,[status(thm)],[c_76402,c_80314]) ).

tcf(c_80506,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))),
    inference(superposition,[status(thm)],[c_76403,c_80314]) ).

tcf(c_80507,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))),
    inference(superposition,[status(thm)],[c_76404,c_80314]) ).

tcf(c_80508,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))),
    inference(superposition,[status(thm)],[c_76405,c_80314]) ).

tcf(c_80509,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_80314]) ).

tcf(c_80510,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_80314]) ).

tcf(c_80511,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_80314]) ).

tcf(c_80512,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_80314]) ).

tcf(c_80513,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_80314]) ).

tcf(c_80514,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_80314]) ).

tcf(c_80515,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_80314]) ).

tcf(c_80516,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_80314]) ).

tcf(c_80517,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_80314]) ).

tcf(c_80527,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_880]) ).

tcf(c_80528,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_608]) ).

tcf(c_80529,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_524]) ).

tcf(c_80530,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_523]) ).

tcf(c_80531,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_347]) ).

tcf(c_80532,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_346]) ).

tcf(c_80533,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_80314,c_254]) ).

tcf(c_80575,plain,
    is_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80397,c_217]) ).

tcf(c_80576,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_880]) ).

tcf(c_80577,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_608]) ).

tcf(c_80578,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_524]) ).

tcf(c_80579,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_523]) ).

tcf(c_80580,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_347]) ).

tcf(c_80581,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_346]) ).

tcf(c_80582,plain,
    number_number_of_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80575,c_254]) ).

tcf(c_80590,plain,
    hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79190,c_78625]) ).

tcf(c_80595,plain,
    ( is_int(hAPP_int_int(iPr_def_13,iPr_def_14))
    | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_79190,c_65]) ).

tcf(c_80597,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))),X0),
    inference(superposition,[status(thm)],[c_79190,c_78759]) ).

tcf(c_80603,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real))
    | ( one_one_real = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_325,c_759]) ).

tcf(c_80605,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(hAPP_int_int(times_times_int(X0),X0))))
      | ( number267125858f_real(X0) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_383,c_759]) ).

tcf(c_80608,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80603,c_1008]) ).

tcf(c_80615,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(zcong(X1,X0)))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1563,c_814]) ).

tcf(c_80619,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,X0),X0)),
    inference(superposition,[status(thm)],[c_913,c_814]) ).

tcf(c_80620,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(X0),X1),X0),X1)),
    inference(superposition,[status(thm)],[c_1699,c_814]) ).

tcf(c_80621,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,X0),min)),
    inference(superposition,[status(thm)],[c_76661,c_814]) ).

tcf(c_80650,plain,
    ! [X0: $i] : hAPP_real_real(minus_minus_real(zero_zero_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(minus_minus_int(pls),X0)),
    inference(superposition,[status(thm)],[c_568,c_878]) ).

tcf(c_80651,plain,
    ! [X0: $i] : hAPP_real_real(minus_minus_real(one_one_real),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(minus_minus_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_78124,c_878]) ).

tcf(c_80652,plain,
    ! [X0: $i] : hAPP_real_real(minus_minus_real(number267125858f_real(X0)),zero_zero_real) = number267125858f_real(hAPP_int_int(minus_minus_int(X0),pls)),
    inference(superposition,[status(thm)],[c_568,c_878]) ).

tcf(c_80653,plain,
    ! [X0: $i] : hAPP_real_real(minus_minus_real(number267125858f_real(X0)),one_one_real) = number267125858f_real(hAPP_int_int(minus_minus_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_78124,c_878]) ).

tcf(c_80658,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(pls),X0)),
    inference(superposition,[status(thm)],[c_574,c_879]) ).

tcf(c_80659,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(min),X0)),
    inference(superposition,[status(thm)],[c_76397,c_879]) ).

tcf(c_80660,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(one_one_int),X0)),
    inference(superposition,[status(thm)],[c_76393,c_879]) ).

tcf(c_80661,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(undefined_int(int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(undefined_int(int)),X0)),
    inference(superposition,[status(thm)],[c_76395,c_879]) ).

tcf(c_80662,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),X1)),
    inference(superposition,[status(thm)],[c_76399,c_879]) ).

tcf(c_80663,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),X2)),
    inference(superposition,[status(thm)],[c_76401,c_879]) ).

tcf(c_80664,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(m),X0)),
    inference(superposition,[status(thm)],[c_76402,c_879]) ).

tcf(c_80665,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(s1),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(s1),X0)),
    inference(superposition,[status(thm)],[c_76403,c_879]) ).

tcf(c_80666,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(s),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(s),X0)),
    inference(superposition,[status(thm)],[c_76404,c_879]) ).

tcf(c_80667,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(t),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(t),X0)),
    inference(superposition,[status(thm)],[c_76405,c_879]) ).

tcf(c_80668,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK9),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK9),X0)),
    inference(superposition,[status(thm)],[c_76406,c_879]) ).

tcf(c_80669,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK10),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK10),X0)),
    inference(superposition,[status(thm)],[c_76407,c_879]) ).

tcf(c_80670,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK11),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK11),X0)),
    inference(superposition,[status(thm)],[c_76408,c_879]) ).

tcf(c_80671,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK13),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK13),X0)),
    inference(superposition,[status(thm)],[c_76409,c_879]) ).

tcf(c_80672,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_14),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_76410,c_879]) ).

tcf(c_80673,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_15),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_15),X0)),
    inference(superposition,[status(thm)],[c_76411,c_879]) ).

tcf(c_80674,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_16),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_16),X0)),
    inference(superposition,[status(thm)],[c_76412,c_879]) ).

tcf(c_80675,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_17),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_17),X0)),
    inference(superposition,[status(thm)],[c_76413,c_879]) ).

tcf(c_80676,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_18),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_18),X0)),
    inference(superposition,[status(thm)],[c_76414,c_879]) ).

tcf(c_80677,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_76415,c_879]) ).

tcf(c_80678,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),X1)),
    inference(superposition,[status(thm)],[c_77366,c_879]) ).

tcf(c_80679,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),X0)),
    inference(superposition,[status(thm)],[c_78203,c_879]) ).

tcf(c_80680,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79573,c_879]) ).

tcf(c_80681,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79414,c_879]) ).

tcf(c_80682,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79557,c_879]) ).

tcf(c_80683,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79437,c_879]) ).

tcf(c_80684,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_79931,c_879]) ).

tcf(c_80685,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_79957,c_879]) ).

tcf(c_80686,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),pls) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),pls)),
    inference(superposition,[status(thm)],[c_574,c_879]) ).

tcf(c_80687,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),min) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),min)),
    inference(superposition,[status(thm)],[c_76397,c_879]) ).

tcf(c_80688,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),one_one_int) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_879]) ).

tcf(c_80689,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),undefined_int(int)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_879]) ).

tcf(c_80690,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),twoSqu1241645765sum2sq(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_879]) ).

tcf(c_80691,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_nat_int(X1,X2)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_879]) ).

tcf(c_80692,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),m)),
    inference(superposition,[status(thm)],[c_76402,c_879]) ).

tcf(c_80693,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),s1) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),s1)),
    inference(superposition,[status(thm)],[c_76403,c_879]) ).

tcf(c_80694,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),s) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),s)),
    inference(superposition,[status(thm)],[c_76404,c_879]) ).

tcf(c_80695,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),t) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),t)),
    inference(superposition,[status(thm)],[c_76405,c_879]) ).

tcf(c_80696,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK9) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_879]) ).

tcf(c_80697,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK10) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_879]) ).

tcf(c_80698,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK11) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_879]) ).

tcf(c_80699,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK13) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_879]) ).

tcf(c_80700,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),iPr_def_14) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_879]) ).

tcf(c_80701,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),iPr_def_15) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_879]) ).

tcf(c_80702,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),iPr_def_16) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_879]) ).

tcf(c_80703,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),iPr_def_17) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_879]) ).

tcf(c_80704,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),iPr_def_18) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_879]) ).

tcf(c_80705,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_879]) ).

tcf(c_80706,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_879]) ).

tcf(c_80707,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK26(iPr_def_14)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_879]) ).

tcf(c_80708,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_879]) ).

tcf(c_80709,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79414,c_879]) ).

tcf(c_80710,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79557,c_879]) ).

tcf(c_80711,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_879]) ).

tcf(c_80712,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79931,c_879]) ).

tcf(c_80713,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_879]) ).

tcf(c_80714,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(minus_minus_int(X1),X0)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_879,c_65]) ).

tcf(c_80839,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(pls,X0))),
    inference(superposition,[status(thm)],[c_80619,c_226]) ).

tcf(c_80841,plain,
    ! [X0: $i] : hBOOL(member_int(min,zcong(pls,X0))),
    inference(superposition,[status(thm)],[c_80621,c_226]) ).

tcf(c_80859,plain,
    is_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80403,c_217]) ).

tcf(c_80860,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_880]) ).

tcf(c_80861,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_608]) ).

tcf(c_80862,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_524]) ).

tcf(c_80863,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_523]) ).

tcf(c_80864,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_347]) ).

tcf(c_80865,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_346]) ).

tcf(c_80866,plain,
    number_number_of_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80859,c_254]) ).

tcf(c_80883,plain,
    is_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80404,c_217]) ).

tcf(c_80884,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_880]) ).

tcf(c_80885,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_608]) ).

tcf(c_80886,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_524]) ).

tcf(c_80887,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_523]) ).

tcf(c_80888,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_347]) ).

tcf(c_80889,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_346]) ).

tcf(c_80890,plain,
    number_number_of_int(hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80883,c_254]) ).

tcf(c_80918,plain,
    is_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80405,c_217]) ).

tcf(c_80919,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_880]) ).

tcf(c_80920,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_608]) ).

tcf(c_80921,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_524]) ).

tcf(c_80922,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_523]) ).

tcf(c_80923,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_347]) ).

tcf(c_80924,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_346]) ).

tcf(c_80925,plain,
    number_number_of_int(hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80918,c_254]) ).

tcf(c_80951,plain,
    is_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80406,c_217]) ).

tcf(c_80952,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_880]) ).

tcf(c_80953,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_608]) ).

tcf(c_80954,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_524]) ).

tcf(c_80955,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_523]) ).

tcf(c_80956,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_347]) ).

tcf(c_80957,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_346]) ).

tcf(c_80958,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80951,c_254]) ).

tcf(c_81021,plain,
    is_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80407,c_217]) ).

tcf(c_81022,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_880]) ).

tcf(c_81023,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_608]) ).

tcf(c_81024,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_524]) ).

tcf(c_81025,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_523]) ).

tcf(c_81026,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_347]) ).

tcf(c_81027,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_346]) ).

tcf(c_81028,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81021,c_254]) ).

tcf(c_81047,plain,
    is_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80408,c_217]) ).

tcf(c_81048,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_880]) ).

tcf(c_81049,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_608]) ).

tcf(c_81050,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_524]) ).

tcf(c_81051,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_523]) ).

tcf(c_81052,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_347]) ).

tcf(c_81053,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_346]) ).

tcf(c_81054,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81047,c_254]) ).

tcf(c_81055,plain,
    is_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80409,c_217]) ).

tcf(c_81056,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_880]) ).

tcf(c_81057,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_608]) ).

tcf(c_81058,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_524]) ).

tcf(c_81059,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_523]) ).

tcf(c_81060,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_347]) ).

tcf(c_81061,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_346]) ).

tcf(c_81062,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81055,c_254]) ).

tcf(c_81075,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80410,c_217]) ).

tcf(c_81080,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(dvd_dvd_int,X1)))
      | hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_929]) ).

tcf(c_81083,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),pls),X0)),
    inference(superposition,[status(thm)],[c_1045,c_929]) ).

tcf(c_81085,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(X0,pls),one_one_int)),
    inference(superposition,[status(thm)],[c_1051,c_929]) ).

tcf(c_81086,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,X0),pls),X0)),
    inference(superposition,[status(thm)],[c_76497,c_929]) ).

tcf(c_81087,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,X0),pls),m)),
    inference(superposition,[status(thm)],[c_76534,c_929]) ).

tcf(c_81088,plain,
    hBOOL(hAPP_int_bool(zcong(iPr_def_17,pls),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76595,c_929]) ).

tcf(c_81089,plain,
    hBOOL(hAPP_int_bool(zcong(iPr_def_17,pls),m)),
    inference(superposition,[status(thm)],[c_76604,c_929]) ).

tcf(c_81090,plain,
    hBOOL(hAPP_int_bool(zcong(one_one_int,pls),min)),
    inference(superposition,[status(thm)],[c_79545,c_929]) ).

tcf(c_81091,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_929]) ).

tcf(c_81102,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(zcong(X1,pls)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_930]) ).

tcf(c_81106,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),X0)),
    inference(superposition,[status(thm)],[c_76661,c_930]) ).

tcf(c_81108,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),pls)),
    inference(superposition,[status(thm)],[c_80621,c_930]) ).

tcf(c_81116,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(zcong(X0,pls)))
      | ( legendre(X0,X1) = pls ) ),
    inference(superposition,[status(thm)],[c_1563,c_940]) ).

tcf(c_81117,plain,
    ! [X0: $i] : legendre(pls,X0) = pls,
    inference(superposition,[status(thm)],[c_815,c_940]) ).

tcf(c_81118,plain,
    ! [X0: $i] : legendre(X0,one_one_int) = pls,
    inference(superposition,[status(thm)],[c_829,c_940]) ).

tcf(c_81119,plain,
    ! [X0: $i] : legendre(X0,X0) = pls,
    inference(superposition,[status(thm)],[c_913,c_940]) ).

tcf(c_81120,plain,
    ! [X0: $i] : legendre(X0,min) = pls,
    inference(superposition,[status(thm)],[c_76661,c_940]) ).

tcf(c_81151,plain,
    hBOOL(member_int(iPr_def_16,zcong(iPr_def_17,pls))),
    inference(superposition,[status(thm)],[c_81088,c_226]) ).

tcf(c_81152,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_17),iPr_def_16)),
    inference(superposition,[status(thm)],[c_81088,c_814]) ).

tcf(c_81153,plain,
    legendre(iPr_def_17,iPr_def_16) = pls,
    inference(superposition,[status(thm)],[c_81088,c_940]) ).

tcf(c_81159,plain,
    hBOOL(member_int(m,zcong(iPr_def_17,pls))),
    inference(superposition,[status(thm)],[c_81089,c_226]) ).

tcf(c_81160,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_17),m)),
    inference(superposition,[status(thm)],[c_81089,c_814]) ).

tcf(c_81161,plain,
    legendre(iPr_def_17,m) = pls,
    inference(superposition,[status(thm)],[c_81089,c_940]) ).

tcf(c_81167,plain,
    ! [X0: $i] : hBOOL(member_int(X0,hAPP_i1948725293t_bool(dvd_dvd_int,min))),
    inference(superposition,[status(thm)],[c_81106,c_226]) ).

tcf(c_81170,plain,
    ! [X0: $i,X1: $i] : sP3(hAPP_i1948725293t_bool(dvd_dvd_int,min),X0,X1),
    inference(superposition,[status(thm)],[c_81106,c_1647]) ).

tcf(c_81175,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80411,c_217]) ).

tcf(c_81176,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_880]) ).

tcf(c_81177,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_608]) ).

tcf(c_81178,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_524]) ).

tcf(c_81179,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_523]) ).

tcf(c_81180,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_347]) ).

tcf(c_81181,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_346]) ).

tcf(c_81182,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81175,c_254]) ).

tcf(c_81195,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80412,c_217]) ).

tcf(c_81196,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_880]) ).

tcf(c_81197,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_608]) ).

tcf(c_81198,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_524]) ).

tcf(c_81199,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_523]) ).

tcf(c_81200,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_347]) ).

tcf(c_81201,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_346]) ).

tcf(c_81202,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81195,c_254]) ).

tcf(c_81220,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80413,c_217]) ).

tcf(c_81221,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_880]) ).

tcf(c_81222,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_608]) ).

tcf(c_81223,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_524]) ).

tcf(c_81224,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_523]) ).

tcf(c_81225,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_347]) ).

tcf(c_81226,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_346]) ).

tcf(c_81227,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81220,c_254]) ).

tcf(c_81228,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80414,c_217]) ).

tcf(c_81229,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_880]) ).

tcf(c_81230,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_608]) ).

tcf(c_81231,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_524]) ).

tcf(c_81232,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_523]) ).

tcf(c_81233,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_347]) ).

tcf(c_81234,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_346]) ).

tcf(c_81235,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_81228,c_254]) ).

tcf(c_81238,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_880]) ).

tcf(c_81239,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_608]) ).

tcf(c_81240,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_524]) ).

tcf(c_81241,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_523]) ).

tcf(c_81242,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_347]) ).

tcf(c_81243,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_346]) ).

tcf(c_81244,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_254]) ).

tcf(c_81254,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_880]) ).

tcf(c_81255,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_608]) ).

tcf(c_81256,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_524]) ).

tcf(c_81257,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_523]) ).

tcf(c_81258,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_347]) ).

tcf(c_81259,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_346]) ).

tcf(c_81260,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80415,c_254]) ).

tcf(c_81281,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_880]) ).

tcf(c_81282,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_608]) ).

tcf(c_81283,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_524]) ).

tcf(c_81284,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_523]) ).

tcf(c_81285,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_347]) ).

tcf(c_81286,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_346]) ).

tcf(c_81287,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_80503,c_254]) ).

tcf(c_81313,plain,
    hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(pls)) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_77431,c_80677]) ).

tcf(c_81314,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_80677,c_879]) ).

tcf(c_81315,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80677,c_80314]) ).

tcf(c_81316,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80677,c_80313]) ).

tcf(c_81317,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_80257]) ).

tcf(c_81318,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_80677,c_388]) ).

tcf(c_81319,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_79563]) ).

tcf(c_81320,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80677,c_79579]) ).

tcf(c_81321,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_80677,c_79562]) ).

tcf(c_81322,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)),
    inference(superposition,[status(thm)],[c_80677,c_382]) ).

tcf(c_81323,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_80677,c_58]) ).

tcf(c_81324,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_879]) ).

tcf(c_81325,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_388]) ).

tcf(c_81326,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_80677,c_79563]) ).

tcf(c_81327,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_382]) ).

tcf(c_81360,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(div_mod_nat(X0),X2)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1364]) ).

tcf(c_81362,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),iPr_def_11)),
    inference(superposition,[status(thm)],[c_76735,c_1364]) ).

tcf(c_81384,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X0,wset(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_1547,c_59643]) ).

tcf(c_81391,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(wset(X0,X1),X0))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(superposition,[status(thm)],[c_81384,c_227]) ).

tcf(c_81400,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X1)))
      | ~ hBOOL(member_int(X0,d22set(X1))) ),
    inference(superposition,[status(thm)],[c_1563,c_1579]) ).

tcf(c_81401,plain,
    ~ hBOOL(member_int(one_one_int,d22set(pls))),
    inference(superposition,[status(thm)],[c_575,c_1579]) ).

tcf(c_81402,plain,
    ~ hBOOL(member_int(pls,d22set(min))),
    inference(superposition,[status(thm)],[c_768,c_1579]) ).

tcf(c_81403,plain,
    ! [X0: $i] :
      ( ~ is_int(X0)
      | ~ hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),d22set(X0))) ),
    inference(superposition,[status(thm)],[c_78137,c_1579]) ).

tcf(c_81404,plain,
    ~ hBOOL(member_int(iPr_def_15,d22set(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78155,c_1579]) ).

tcf(c_81405,plain,
    ~ hBOOL(member_int(iPr_def_16,d22set(iPr_def_15))),
    inference(superposition,[status(thm)],[c_78154,c_1579]) ).

tcf(c_81406,plain,
    ~ hBOOL(member_int(iPr_def_18,d22set(iPr_def_17))),
    inference(superposition,[status(thm)],[c_78153,c_1579]) ).

tcf(c_81407,plain,
    ~ hBOOL(member_int(t,d22set(pls))),
    inference(superposition,[status(thm)],[c_80152,c_1579]) ).

tcf(c_81408,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(member_int(X0,d22set(X1)))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_1579]) ).

tcf(c_81409,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(member_int(X0,d22set(one_one_int))) ),
    inference(superposition,[status(thm)],[c_59643,c_1579]) ).

tcf(c_81426,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(X0,X1,X2)
      | hBOOL(member_int(sK39(X0,X1,X2),hAPP_i1948725293t_bool(ord_less_eq_int,pls))) ),
    inference(superposition,[status(thm)],[c_1648,c_226]) ).

tcf(c_81427,plain,
    ! [X0: $i,X1: $i] : sP3(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0,X1),
    inference(superposition,[status(thm)],[c_1648,c_1647]) ).

tcf(c_81464,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_80705,c_879]) ).

tcf(c_81465,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_80314]) ).

tcf(c_81466,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_80313]) ).

tcf(c_81467,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_80257]) ).

tcf(c_81468,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_80705,c_388]) ).

tcf(c_81469,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80705,c_79563]) ).

tcf(c_81470,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80705,c_79579]) ).

tcf(c_81471,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_79562]) ).

tcf(c_81472,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_80705,c_382]) ).

tcf(c_81473,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80705,c_58]) ).

tcf(c_81474,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_879]) ).

tcf(c_81475,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_388]) ).

tcf(c_81476,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_79563]) ).

tcf(c_81477,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_382]) ).

tcf(c_81478,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(sK30(iPr_def_19))),sK30(iPr_def_19)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_80677]) ).

tcf(c_81500,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),pls)))),
    inference(superposition,[status(thm)],[c_574,c_81315]) ).

tcf(c_81501,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),min)))),
    inference(superposition,[status(thm)],[c_76397,c_81315]) ).

tcf(c_81502,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)))),
    inference(superposition,[status(thm)],[c_76393,c_81315]) ).

tcf(c_81503,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),undefined_int(int))))),
    inference(superposition,[status(thm)],[c_76395,c_81315]) ).

tcf(c_81504,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0))))),
    inference(superposition,[status(thm)],[c_76399,c_81315]) ).

tcf(c_81505,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))))),
    inference(superposition,[status(thm)],[c_76401,c_81315]) ).

tcf(c_81506,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))),
    inference(superposition,[status(thm)],[c_76402,c_81315]) ).

tcf(c_81507,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),s1)))),
    inference(superposition,[status(thm)],[c_76403,c_81315]) ).

tcf(c_81508,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),s)))),
    inference(superposition,[status(thm)],[c_76404,c_81315]) ).

tcf(c_81509,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),t)))),
    inference(superposition,[status(thm)],[c_76405,c_81315]) ).

tcf(c_81510,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK9)))),
    inference(superposition,[status(thm)],[c_76406,c_81315]) ).

tcf(c_81511,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK10)))),
    inference(superposition,[status(thm)],[c_76407,c_81315]) ).

tcf(c_81512,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK11)))),
    inference(superposition,[status(thm)],[c_76408,c_81315]) ).

tcf(c_81513,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK13)))),
    inference(superposition,[status(thm)],[c_76409,c_81315]) ).

tcf(c_81514,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_76410,c_81315]) ).

tcf(c_81515,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_15)))),
    inference(superposition,[status(thm)],[c_76411,c_81315]) ).

tcf(c_81516,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_16)))),
    inference(superposition,[status(thm)],[c_76412,c_81315]) ).

tcf(c_81517,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_17)))),
    inference(superposition,[status(thm)],[c_76413,c_81315]) ).

tcf(c_81518,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_18)))),
    inference(superposition,[status(thm)],[c_76414,c_81315]) ).

tcf(c_81519,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76415,c_81315]) ).

tcf(c_81520,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))))),
    inference(superposition,[status(thm)],[c_77366,c_81315]) ).

tcf(c_81521,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK26(iPr_def_14))))),
    inference(superposition,[status(thm)],[c_78203,c_81315]) ).

tcf(c_81523,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79414,c_81315]) ).

tcf(c_81525,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79437,c_81315]) ).

tcf(c_81526,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79931,c_81315]) ).

tcf(c_81527,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79957,c_81315]) ).

tcf(c_81528,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80677,c_81315]) ).

tcf(c_81529,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80705,c_81315]) ).

tcf(c_81530,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_880]) ).

tcf(c_81531,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_608]) ).

tcf(c_81532,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_524]) ).

tcf(c_81533,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_523]) ).

tcf(c_81534,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_347]) ).

tcf(c_81535,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_346]) ).

tcf(c_81536,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_81315,c_254]) ).

tcf(c_81597,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(pls),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_574,c_81465]) ).

tcf(c_81598,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(min),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76397,c_81465]) ).

tcf(c_81599,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(one_one_int),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76393,c_81465]) ).

tcf(c_81600,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(undefined_int(int)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76395,c_81465]) ).

tcf(c_81601,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76399,c_81465]) ).

tcf(c_81602,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76401,c_81465]) ).

tcf(c_81603,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76402,c_81465]) ).

tcf(c_81604,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(s1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76403,c_81465]) ).

tcf(c_81605,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(s),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76404,c_81465]) ).

tcf(c_81606,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(t),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76405,c_81465]) ).

tcf(c_81607,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK9),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76406,c_81465]) ).

tcf(c_81608,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK10),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76407,c_81465]) ).

tcf(c_81609,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK11),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76408,c_81465]) ).

tcf(c_81610,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK13),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76409,c_81465]) ).

tcf(c_81611,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_14),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76410,c_81465]) ).

tcf(c_81612,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_15),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76411,c_81465]) ).

tcf(c_81613,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_16),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76412,c_81465]) ).

tcf(c_81614,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_17),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76413,c_81465]) ).

tcf(c_81615,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_18),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76414,c_81465]) ).

tcf(c_81617,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_77366,c_81465]) ).

tcf(c_81618,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_78203,c_81465]) ).

tcf(c_81620,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79414,c_81465]) ).

tcf(c_81622,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_81465]) ).

tcf(c_81623,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79931,c_81465]) ).

tcf(c_81624,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79957,c_81465]) ).

tcf(c_81625,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80677,c_81465]) ).

tcf(c_81626,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_81465]) ).

tcf(c_81627,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_880]) ).

tcf(c_81628,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_608]) ).

tcf(c_81629,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_524]) ).

tcf(c_81630,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_523]) ).

tcf(c_81631,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_347]) ).

tcf(c_81632,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_346]) ).

tcf(c_81633,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_254]) ).

tcf(c_81706,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_880]) ).

tcf(c_81707,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_608]) ).

tcf(c_81708,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_524]) ).

tcf(c_81709,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_523]) ).

tcf(c_81710,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_347]) ).

tcf(c_81711,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_346]) ).

tcf(c_81712,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_254]) ).

tcf(c_81721,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_253,c_79818]) ).

tcf(c_81723,plain,
    hAPP_int_int(times_times_int(number_number_of_int(pls)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_1004,c_79818]) ).

tcf(c_81724,plain,
    hAPP_int_int(times_times_int(number_number_of_int(m)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_59637,c_79818]) ).

tcf(c_81725,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79818,c_81465]) ).

tcf(c_81726,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),
    inference(superposition,[status(thm)],[c_79818,c_81315]) ).

tcf(c_81727,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79818,c_879]) ).

tcf(c_81728,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79818,c_80314]) ).

tcf(c_81729,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79818,c_80313]) ).

tcf(c_81730,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79818,c_80257]) ).

tcf(c_81731,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79818,c_388]) ).

tcf(c_81732,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79818,c_79563]) ).

tcf(c_81733,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79818,c_79579]) ).

tcf(c_81734,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_79818,c_79562]) ).

tcf(c_81735,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79818,c_382]) ).

tcf(c_81736,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79818,c_58]) ).

tcf(c_81737,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79818,c_879]) ).

tcf(c_81738,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79818,c_388]) ).

tcf(c_81739,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79818,c_79563]) ).

tcf(c_81740,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79818,c_382]) ).

tcf(c_81741,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_79573]) ).

tcf(c_81742,plain,
    hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79818,c_79414]) ).

tcf(c_81743,plain,
    hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = pls,
    inference(light_normalisation,[status(thm)],[c_81723,c_574]) ).

tcf(c_81744,plain,
    number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_81724,c_59637,c_76402]) ).

tcf(c_81747,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_81742,c_76415]) ).

tcf(c_81748,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_81741,c_76415]) ).

tcf(c_81806,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_253,c_81728]) ).

tcf(c_81808,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_574,c_81728]) ).

tcf(c_81809,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76397,c_81728]) ).

tcf(c_81810,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76393,c_81728]) ).

tcf(c_81811,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76395,c_81728]) ).

tcf(c_81812,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76399,c_81728]) ).

tcf(c_81813,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76401,c_81728]) ).

tcf(c_81814,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76402,c_81728]) ).

tcf(c_81815,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76403,c_81728]) ).

tcf(c_81816,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76404,c_81728]) ).

tcf(c_81817,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76405,c_81728]) ).

tcf(c_81818,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76406,c_81728]) ).

tcf(c_81819,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76407,c_81728]) ).

tcf(c_81820,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76408,c_81728]) ).

tcf(c_81821,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76409,c_81728]) ).

tcf(c_81822,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76410,c_81728]) ).

tcf(c_81823,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76411,c_81728]) ).

tcf(c_81824,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76412,c_81728]) ).

tcf(c_81825,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76413,c_81728]) ).

tcf(c_81826,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76414,c_81728]) ).

tcf(c_81827,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76415,c_81728]) ).

tcf(c_81828,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_77366,c_81728]) ).

tcf(c_81829,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_78203,c_81728]) ).

tcf(c_81831,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79414,c_81728]) ).

tcf(c_81833,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79437,c_81728]) ).

tcf(c_81834,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79818,c_81728]) ).

tcf(c_81835,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79931,c_81728]) ).

tcf(c_81836,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79957,c_81728]) ).

tcf(c_81837,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80677,c_81728]) ).

tcf(c_81838,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80705,c_81728]) ).

tcf(c_81839,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_880]) ).

tcf(c_81840,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_608]) ).

tcf(c_81841,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_524]) ).

tcf(c_81842,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_523]) ).

tcf(c_81843,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_347]) ).

tcf(c_81844,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_346]) ).

tcf(c_81845,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81728,c_254]) ).

tcf(c_81846,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),
    inference(light_normalisation,[status(thm)],[c_81814,c_59637]) ).

tcf(c_81975,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5674,c_1488]) ).

tcf(c_81976,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0)
      | ~ is_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5674,c_1487]) ).

tcf(c_81977,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1)),twoSqu1154269391sum2sq))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_5674,c_226]) ).

tcf(c_81981,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_81976,c_61]) ).

tcf(c_81985,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(X0,X1))))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_81975,c_61]) ).

tcf(c_81992,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_14654,c_59634,c_59635]) ).

tcf(c_81994,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),pls)) ),
    inference(superposition,[status(thm)],[c_491,c_81992]) ).

tcf(c_81997,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),iPr_def_11)),zero_zero_real)),
    inference(light_normalisation,[status(thm)],[c_14655,c_59634,c_59635]) ).

tcf(c_81998,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_495,c_81997]) ).

tcf(c_82001,plain,
    hBOOL(member_int(iPr_def_16,zcong(pls,iPr_def_17))),
    inference(superposition,[status(thm)],[c_81152,c_226]) ).

tcf(c_82010,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_880]) ).

tcf(c_82011,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_608]) ).

tcf(c_82012,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_524]) ).

tcf(c_82013,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_523]) ).

tcf(c_82014,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_347]) ).

tcf(c_82015,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_346]) ).

tcf(c_82016,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_81827,c_254]) ).

tcf(c_82021,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(demodulation,[status(thm)],[c_80430,c_253,c_79557,c_79573]) ).

tcf(c_82044,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_82021]) ).

tcf(c_82046,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_82021]) ).

tcf(c_82047,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_82021]) ).

tcf(c_82048,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_82021]) ).

tcf(c_82049,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_82021]) ).

tcf(c_82050,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_82021]) ).

tcf(c_82051,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_82021]) ).

tcf(c_82053,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_82021,c_1042]) ).

tcf(c_82054,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_82021,c_833]) ).

tcf(c_82057,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_82021,c_76498]) ).

tcf(c_82059,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_82021,c_833]) ).

tcf(c_82060,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_82021,c_79573]) ).

tcf(c_82061,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_82021,c_79414]) ).

tcf(c_82067,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82051,c_81467]) ).

tcf(c_82068,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82050,c_81317]) ).

tcf(c_82069,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82049,c_80268]) ).

tcf(c_82070,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82048,c_80267]) ).

tcf(c_82071,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82046,c_80266]) ).

tcf(c_82072,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82044,c_80264]) ).

tcf(c_82073,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_82047,c_81730]) ).

tcf(c_82108,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_574,c_80424]) ).

tcf(c_82109,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76397,c_80424]) ).

tcf(c_82110,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_80424]) ).

tcf(c_82111,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76395,c_80424]) ).

tcf(c_82113,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76401,c_80424]) ).

tcf(c_82114,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_80424]) ).

tcf(c_82115,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76403,c_80424]) ).

tcf(c_82116,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76404,c_80424]) ).

tcf(c_82117,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76405,c_80424]) ).

tcf(c_82118,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76406,c_80424]) ).

tcf(c_82119,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76407,c_80424]) ).

tcf(c_82120,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76408,c_80424]) ).

tcf(c_82121,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76409,c_80424]) ).

tcf(c_82122,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76410,c_80424]) ).

tcf(c_82123,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76411,c_80424]) ).

tcf(c_82124,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76412,c_80424]) ).

tcf(c_82125,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76413,c_80424]) ).

tcf(c_82126,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76414,c_80424]) ).

tcf(c_82128,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_77366,c_80424]) ).

tcf(c_82129,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78203,c_80424]) ).

tcf(c_82131,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_80424]) ).

tcf(c_82133,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_80424]) ).

tcf(c_82134,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_80424]) ).

tcf(c_82135,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_80424]) ).

tcf(c_82136,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_80424]) ).

tcf(c_82137,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_80424]) ).

tcf(c_82138,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_80424]) ).

tcf(c_82140,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_82114,c_59637]) ).

tcf(c_82141,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_82110,c_76995]) ).

tcf(c_82142,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_82129,c_80262]) ).

tcf(c_82143,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(light_normalisation,[status(thm)],[c_82111,c_80258]) ).

tcf(c_82144,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(light_normalisation,[status(thm)],[c_82128,c_80261]) ).

tcf(c_82145,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(light_normalisation,[status(thm)],[c_82113,c_80260]) ).

tcf(c_82148,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82136,c_80268]) ).

tcf(c_82149,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82135,c_80267]) ).

tcf(c_82150,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82133,c_80266]) ).

tcf(c_82151,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82131,c_80264]) ).

tcf(c_82191,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_574,c_80425]) ).

tcf(c_82192,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76397,c_80425]) ).

tcf(c_82193,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_80425]) ).

tcf(c_82194,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76395,c_80425]) ).

tcf(c_82196,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76401,c_80425]) ).

tcf(c_82197,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_80425]) ).

tcf(c_82198,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76403,c_80425]) ).

tcf(c_82199,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76404,c_80425]) ).

tcf(c_82200,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76405,c_80425]) ).

tcf(c_82201,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76406,c_80425]) ).

tcf(c_82202,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76407,c_80425]) ).

tcf(c_82203,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76408,c_80425]) ).

tcf(c_82204,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76409,c_80425]) ).

tcf(c_82205,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76410,c_80425]) ).

tcf(c_82206,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76411,c_80425]) ).

tcf(c_82207,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76412,c_80425]) ).

tcf(c_82208,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76413,c_80425]) ).

tcf(c_82209,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76414,c_80425]) ).

tcf(c_82211,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_77366,c_80425]) ).

tcf(c_82212,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78203,c_80425]) ).

tcf(c_82214,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_80425]) ).

tcf(c_82216,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_80425]) ).

tcf(c_82217,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_80425]) ).

tcf(c_82218,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_80425]) ).

tcf(c_82219,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_80425]) ).

tcf(c_82220,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_80425]) ).

tcf(c_82221,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_80425]) ).

tcf(c_82224,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_82197,c_59637]) ).

tcf(c_82225,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_82193,c_76995]) ).

tcf(c_82226,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_82212,c_80262]) ).

tcf(c_82227,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(light_normalisation,[status(thm)],[c_82194,c_80258]) ).

tcf(c_82228,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(light_normalisation,[status(thm)],[c_82211,c_80261]) ).

tcf(c_82229,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(light_normalisation,[status(thm)],[c_82196,c_80260]) ).

tcf(c_82232,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82219,c_80268]) ).

tcf(c_82233,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82218,c_80267]) ).

tcf(c_82234,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82216,c_80266]) ).

tcf(c_82235,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82214,c_80264]) ).

tcf(c_82285,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_79901]) ).

tcf(c_82287,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))
      | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_79901,c_65]) ).

tcf(c_82288,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))
      | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_79901,c_76880]) ).

tcf(c_82299,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)) != X0 ) ),
    inference(superposition,[status(thm)],[c_14792,c_517]) ).

tcf(c_82300,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0) = hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),
    inference(superposition,[status(thm)],[c_14792,c_373]) ).

tcf(c_82301,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_14792,c_521]) ).

tcf(c_82302,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_14792,c_389]) ).

tcf(c_82315,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),iPr_def_11) = hAPP_nat_nat(times_times_nat(iPr_def_11),X0),
    inference(light_normalisation,[status(thm)],[c_14796,c_59634,c_59635,c_79342]) ).

tcf(c_82316,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(X0),X0) = hAPP_nat_nat(power_power_nat(X0),iPr_def_11),
    inference(light_normalisation,[status(thm)],[c_14804,c_59634,c_59635]) ).

tcf(c_82319,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(power_power_nat(X0),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82316,c_1408]) ).

tcf(c_82321,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(power_power_nat(X0),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82316,c_1409]) ).

tcf(c_82322,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),iPr_def_11) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_82316,c_1416]) ).

tcf(c_82324,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),X0) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_82316,c_1684]) ).

tcf(c_82327,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(power_power_nat(X0),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82316,c_1044]) ).

tcf(c_82329,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X0) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_82316,c_1065]) ).

tcf(c_82330,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_nat_nat(times_times_nat(zero_zero_nat),zero_zero_nat) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_82316,c_1063]) ).

tcf(c_82331,plain,
    hAPP_nat_nat(times_times_nat(one_one_nat),one_one_nat) = one_one_nat,
    inference(superposition,[status(thm)],[c_82316,c_1222]) ).

tcf(c_82349,plain,
    hBOOL(member_int(m,zcong(pls,iPr_def_17))),
    inference(superposition,[status(thm)],[c_81160,c_226]) ).

tcf(c_82370,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_574,c_80427]) ).

tcf(c_82371,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76397,c_80427]) ).

tcf(c_82372,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_80427]) ).

tcf(c_82373,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76395,c_80427]) ).

tcf(c_82375,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76401,c_80427]) ).

tcf(c_82376,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_80427]) ).

tcf(c_82377,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76403,c_80427]) ).

tcf(c_82378,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76404,c_80427]) ).

tcf(c_82379,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76405,c_80427]) ).

tcf(c_82380,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76406,c_80427]) ).

tcf(c_82381,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76407,c_80427]) ).

tcf(c_82382,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76408,c_80427]) ).

tcf(c_82383,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76409,c_80427]) ).

tcf(c_82384,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76410,c_80427]) ).

tcf(c_82385,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76411,c_80427]) ).

tcf(c_82386,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76412,c_80427]) ).

tcf(c_82387,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76413,c_80427]) ).

tcf(c_82388,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76414,c_80427]) ).

tcf(c_82390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_77366,c_80427]) ).

tcf(c_82391,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78203,c_80427]) ).

tcf(c_82393,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_80427]) ).

tcf(c_82395,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_80427]) ).

tcf(c_82396,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_80427]) ).

tcf(c_82397,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_80427]) ).

tcf(c_82398,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_80427]) ).

tcf(c_82399,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_80427]) ).

tcf(c_82400,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_80427]) ).

tcf(c_82403,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_82376,c_59637]) ).

tcf(c_82404,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_82372,c_76995]) ).

tcf(c_82405,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_82391,c_80262]) ).

tcf(c_82406,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(light_normalisation,[status(thm)],[c_82373,c_80258]) ).

tcf(c_82407,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(light_normalisation,[status(thm)],[c_82390,c_80261]) ).

tcf(c_82408,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(light_normalisation,[status(thm)],[c_82375,c_80260]) ).

tcf(c_82411,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82398,c_80268]) ).

tcf(c_82412,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82397,c_80267]) ).

tcf(c_82413,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82395,c_80266]) ).

tcf(c_82414,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82393,c_80264]) ).

tcf(c_82449,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_574,c_80428]) ).

tcf(c_82450,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76397,c_80428]) ).

tcf(c_82451,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_80428]) ).

tcf(c_82452,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76395,c_80428]) ).

tcf(c_82454,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76401,c_80428]) ).

tcf(c_82455,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_80428]) ).

tcf(c_82456,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76403,c_80428]) ).

tcf(c_82457,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76404,c_80428]) ).

tcf(c_82458,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76405,c_80428]) ).

tcf(c_82459,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76406,c_80428]) ).

tcf(c_82460,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76407,c_80428]) ).

tcf(c_82461,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76408,c_80428]) ).

tcf(c_82462,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76409,c_80428]) ).

tcf(c_82463,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76410,c_80428]) ).

tcf(c_82464,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76411,c_80428]) ).

tcf(c_82465,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76412,c_80428]) ).

tcf(c_82466,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76413,c_80428]) ).

tcf(c_82467,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76414,c_80428]) ).

tcf(c_82469,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_77366,c_80428]) ).

tcf(c_82470,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78203,c_80428]) ).

tcf(c_82472,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_80428]) ).

tcf(c_82474,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_80428]) ).

tcf(c_82475,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79818,c_80428]) ).

tcf(c_82476,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_80428]) ).

tcf(c_82477,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_80428]) ).

tcf(c_82478,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_80428]) ).

tcf(c_82479,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_80428]) ).

tcf(c_82481,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80428,c_1042]) ).

tcf(c_82482,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80428,c_833]) ).

tcf(c_82484,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_80428,c_76535]) ).

tcf(c_82485,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80428,c_76498]) ).

tcf(c_82486,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80428,c_1045]) ).

tcf(c_82487,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80428,c_833]) ).

tcf(c_82488,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_82455,c_59637]) ).

tcf(c_82489,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_82451,c_76995]) ).

tcf(c_82490,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_82470,c_80262]) ).

tcf(c_82491,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(light_normalisation,[status(thm)],[c_82452,c_80258]) ).

tcf(c_82492,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(light_normalisation,[status(thm)],[c_82469,c_80261]) ).

tcf(c_82493,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(light_normalisation,[status(thm)],[c_82454,c_80260]) ).

tcf(c_82496,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82477,c_80268]) ).

tcf(c_82497,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82476,c_80267]) ).

tcf(c_82498,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_82474,c_80266]) ).

tcf(c_82499,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_82472,c_80264]) ).

tcf(c_82683,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(superposition,[status(thm)],[c_574,c_80527]) ).

tcf(c_82684,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76397,c_80527]) ).

tcf(c_82685,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_80527]) ).

tcf(c_82689,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)),
    inference(superposition,[status(thm)],[c_76402,c_80527]) ).

tcf(c_82690,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_80527]) ).

tcf(c_82691,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)),
    inference(superposition,[status(thm)],[c_76404,c_80527]) ).

tcf(c_82692,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)),
    inference(superposition,[status(thm)],[c_76405,c_80527]) ).

tcf(c_82693,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_80527]) ).

tcf(c_82694,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_80527]) ).

tcf(c_82695,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_80527]) ).

tcf(c_82696,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_80527]) ).

tcf(c_82697,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_80527]) ).

tcf(c_82698,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_80527]) ).

tcf(c_82699,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_80527]) ).

tcf(c_82700,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_80527]) ).

tcf(c_82701,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_80527]) ).

tcf(c_82735,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(superposition,[status(thm)],[c_574,c_80528]) ).

tcf(c_82736,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76397,c_80528]) ).

tcf(c_82737,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_80528]) ).

tcf(c_82741,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)),
    inference(superposition,[status(thm)],[c_76402,c_80528]) ).

tcf(c_82742,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_80528]) ).

tcf(c_82743,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)),
    inference(superposition,[status(thm)],[c_76404,c_80528]) ).

tcf(c_82744,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)),
    inference(superposition,[status(thm)],[c_76405,c_80528]) ).

tcf(c_82745,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_80528]) ).

tcf(c_82746,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_80528]) ).

tcf(c_82747,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_80528]) ).

tcf(c_82748,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_80528]) ).

tcf(c_82749,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_80528]) ).

tcf(c_82750,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_80528]) ).

tcf(c_82751,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_80528]) ).

tcf(c_82752,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_80528]) ).

tcf(c_82753,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_80528]) ).

tcf(c_82788,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(superposition,[status(thm)],[c_574,c_80530]) ).

tcf(c_82789,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76397,c_80530]) ).

tcf(c_82790,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_80530]) ).

tcf(c_82794,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)),
    inference(superposition,[status(thm)],[c_76402,c_80530]) ).

tcf(c_82795,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_80530]) ).

tcf(c_82796,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)),
    inference(superposition,[status(thm)],[c_76404,c_80530]) ).

tcf(c_82797,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)),
    inference(superposition,[status(thm)],[c_76405,c_80530]) ).

tcf(c_82798,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_80530]) ).

tcf(c_82799,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_80530]) ).

tcf(c_82800,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_80530]) ).

tcf(c_82801,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_80530]) ).

tcf(c_82802,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_80530]) ).

tcf(c_82803,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_80530]) ).

tcf(c_82804,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_80530]) ).

tcf(c_82805,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_80530]) ).

tcf(c_82806,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_80530]) ).

tcf(c_82837,plain,
    ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))
    | ~ is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_79904,c_65]) ).

tcf(c_82838,plain,
    ( is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))
    | ~ is_int(m) ),
    inference(superposition,[status(thm)],[c_79904,c_76880]) ).

tcf(c_82839,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(X0),X0) = hAPP_nat_real(power_power_real(X0),iPr_def_11),
    inference(light_normalisation,[status(thm)],[c_14806,c_59634,c_59635]) ).

tcf(c_82843,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),iPr_def_11)))
      | ( X0 = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_82839,c_759]) ).

tcf(c_82846,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_nat_real(power_power_real(X0),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82839,c_1043]) ).

tcf(c_82848,plain,
    ! [X0: $i] : number267125858f_real(hAPP_int_int(times_times_int(X0),X0)) = hAPP_nat_real(power_power_real(number267125858f_real(X0)),iPr_def_11),
    inference(superposition,[status(thm)],[c_82839,c_383]) ).

tcf(c_82849,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),X0) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_82839,c_489]) ).

tcf(c_82850,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_real_real(times_times_real(zero_zero_real),zero_zero_real) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_82839,c_495]) ).

tcf(c_82851,plain,
    hAPP_real_real(times_times_real(one_one_real),one_one_real) = one_one_real,
    inference(superposition,[status(thm)],[c_82839,c_671]) ).

tcf(c_82861,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),iPr_def_11),
    inference(light_normalisation,[status(thm)],[c_14808,c_59634,c_59635]) ).

tcf(c_82862,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),
    inference(demodulation,[status(thm)],[c_81827,c_82861]) ).

tcf(c_82863,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),
    inference(demodulation,[status(thm)],[c_81728,c_82861]) ).

tcf(c_82864,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_79818,c_82861]) ).

tcf(c_82865,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80415,c_82861]) ).

tcf(c_82866,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81228,c_82861]) ).

tcf(c_82867,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81220,c_82861]) ).

tcf(c_82868,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81195,c_82861]) ).

tcf(c_82869,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81175,c_82861]) ).

tcf(c_82870,plain,
    is_int(hAPP_int_int(times_times_int(sK13),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81055,c_82861]) ).

tcf(c_82871,plain,
    is_int(hAPP_int_int(times_times_int(sK11),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81047,c_82861]) ).

tcf(c_82872,plain,
    is_int(hAPP_int_int(times_times_int(sK10),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_81021,c_82861]) ).

tcf(c_82873,plain,
    is_int(hAPP_int_int(times_times_int(sK9),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80951,c_82861]) ).

tcf(c_82874,plain,
    is_int(hAPP_int_int(times_times_int(t),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80918,c_82861]) ).

tcf(c_82875,plain,
    is_int(hAPP_int_int(times_times_int(s),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80883,c_82861]) ).

tcf(c_82876,plain,
    is_int(hAPP_int_int(times_times_int(s1),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80859,c_82861]) ).

tcf(c_82877,plain,
    is_int(hAPP_int_int(times_times_int(min),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80575,c_82861]) ).

tcf(c_82888,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),iPr_def_11),hAPP_int_int(times_times_int(X1),X0)),X0)),
    inference(superposition,[status(thm)],[c_82861,c_833]) ).

tcf(c_82889,plain,
    ! [X0: $i] :
      ( is_int(hAPP_nat_int(power_power_int(X0),iPr_def_11))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_82861,c_76863]) ).

tcf(c_82890,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_nat_int(power_power_int(X0),iPr_def_11),hAPP_i1948725293t_bool(dvd_dvd_int,X0))),
    inference(superposition,[status(thm)],[c_82861,c_76535]) ).

tcf(c_82892,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X0),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_1045]) ).

tcf(c_82893,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_nat_int(power_power_int(X1),iPr_def_11)),X1)),
    inference(superposition,[status(thm)],[c_82861,c_833]) ).

tcf(c_82894,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),X0)) = hAPP_nat_int(power_power_int(number_number_of_int(X0)),iPr_def_11),
    inference(superposition,[status(thm)],[c_82861,c_382]) ).

tcf(c_82895,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X0)),iPr_def_11)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_82861,c_78759]) ).

tcf(c_82902,plain,
    hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),sK30(iPr_def_19)) = number_number_of_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_79573]) ).

tcf(c_82903,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(sK30(iPr_def_19))) = number_number_of_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_79414]) ).

tcf(c_82904,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_82861,c_78432]) ).

tcf(c_82905,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_78420]) ).

tcf(c_82906,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_78405]) ).

tcf(c_82907,plain,
    hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_78397]) ).

tcf(c_82908,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),X0)) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82861,c_76401]) ).

tcf(c_82909,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),X0)),
    inference(superposition,[status(thm)],[c_82861,c_67]) ).

tcf(c_82910,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(times_times_int(pls),pls) = pls ) ),
    inference(superposition,[status(thm)],[c_82861,c_491]) ).

tcf(c_82913,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_79175]) ).

tcf(c_82914,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(times_times_int(X0),X0))),
    inference(superposition,[status(thm)],[c_82861,c_79141]) ).

tcf(c_82916,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),X0) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_78501]) ).

tcf(c_82917,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_76355]) ).

tcf(c_82918,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_59645]) ).

tcf(c_82919,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(times_times_int(X1),X1)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_59645]) ).

tcf(c_82920,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)) = number_number_of_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(light_normalisation,[status(thm)],[c_82903,c_76415]) ).

tcf(c_82935,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(s),s)) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(light_normalisation,[status(thm)],[c_16376,c_59636]) ).

tcf(c_82936,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(hAPP_int_int(times_times_int(s),s)) ),
    inference(superposition,[status(thm)],[c_82935,c_65]) ).

tcf(c_82937,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
    | ~ is_int(hAPP_int_int(times_times_int(s),s)) ),
    inference(superposition,[status(thm)],[c_82935,c_78137]) ).

tcf(c_82938,plain,
    is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_82935,c_77937]) ).

tcf(c_82939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(s),s)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))) != hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_82935,c_76515]) ).

tcf(c_82940,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(s),s)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))) != pls,
    inference(superposition,[status(thm)],[c_82935,c_76368]) ).

tcf(c_82948,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),one_one_int)),X0) = pls,
    inference(superposition,[status(thm)],[c_49,c_46104]) ).

tcf(c_82949,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),pls)),X0) = pls,
    inference(superposition,[status(thm)],[c_57,c_46104]) ).

tcf(c_82950,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),undefined_int(int))),X0) = pls,
    inference(superposition,[status(thm)],[c_51,c_46104]) ).

tcf(c_82951,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X2),multInv(X0,X1))),X2) = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_46104]) ).

tcf(c_82952,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),zfact(X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_46104]) ).

tcf(c_82953,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_79191,c_46104]) ).

tcf(c_82954,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),min)),X0) = pls,
    inference(superposition,[status(thm)],[c_56,c_46104]) ).

tcf(c_82955,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),number_number_of_int(X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_46104]) ).

tcf(c_82956,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X2),legendre(X0,X1))),X2) = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_46104]) ).

tcf(c_82957,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),twoSqu1241645765sum2sq(X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_61,c_46104]) ).

tcf(c_82958,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X2),inv(X0,X1))),X2) = pls )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_46104]) ).

tcf(c_82959,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(X2,X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_46104]) ).

tcf(c_82960,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(X1,X2))),X0) = pls,
    inference(superposition,[status(thm)],[c_67,c_46104]) ).

tcf(c_82961,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),m)),X0) = pls,
    inference(superposition,[status(thm)],[c_70,c_46104]) ).

tcf(c_82962,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),s1)),X0) = pls,
    inference(superposition,[status(thm)],[c_71,c_46104]) ).

tcf(c_82963,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),s)),X0) = pls,
    inference(superposition,[status(thm)],[c_72,c_46104]) ).

tcf(c_82964,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),t)),X0) = pls,
    inference(superposition,[status(thm)],[c_73,c_46104]) ).

tcf(c_82965,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK9)),X0) = pls,
    inference(superposition,[status(thm)],[c_113,c_46104]) ).

tcf(c_82966,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK10)),X0) = pls,
    inference(superposition,[status(thm)],[c_451,c_46104]) ).

tcf(c_82967,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK11)),X0) = pls,
    inference(superposition,[status(thm)],[c_459,c_46104]) ).

tcf(c_82968,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK13)),X0) = pls,
    inference(superposition,[status(thm)],[c_735,c_46104]) ).

tcf(c_82969,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(quadRes(X1)))
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK15(X1,X2))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_77479,c_46104]) ).

tcf(c_82970,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK22(X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_46104]) ).

tcf(c_82971,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK23(X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_46104]) ).

tcf(c_82972,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,X2))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_78002,c_46104]) ).

tcf(c_82973,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_46104]) ).

tcf(c_82974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X1,X2,X3)
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK38(X1,X2,X3))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_1651,c_46104]) ).

tcf(c_82975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X1,X2,X3)
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK39(X1,X2,X3))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_1652,c_46104]) ).

tcf(c_82978,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),X0) = pls,
    inference(superposition,[status(thm)],[c_76346,c_46104]) ).

tcf(c_82979,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),iPr_def_15)),X0) = pls,
    inference(superposition,[status(thm)],[c_76347,c_46104]) ).

tcf(c_82980,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),iPr_def_16)),X0) = pls,
    inference(superposition,[status(thm)],[c_76348,c_46104]) ).

tcf(c_82981,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),iPr_def_17)),X0) = pls,
    inference(superposition,[status(thm)],[c_76349,c_46104]) ).

tcf(c_82982,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),iPr_def_18)),X0) = pls,
    inference(superposition,[status(thm)],[c_76350,c_46104]) ).

tcf(c_82983,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X0) = pls,
    inference(superposition,[status(thm)],[c_76385,c_46104]) ).

tcf(c_82984,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76383,c_46104]) ).

tcf(c_82985,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,min)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76382,c_46104]) ).

tcf(c_82986,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76384,c_46104]) ).

tcf(c_82987,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK30(hAPP_i1948725293t_bool(ord_less_int,X0)))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_46104]) ).

tcf(c_82988,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),X2))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_46104]) ).

tcf(c_82989,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_77054,c_46104]) ).

tcf(c_82990,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(cOMBC_int_int_bool(ord_less_int,pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_77703,c_46104]) ).

tcf(c_82991,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77831,c_46104]) ).

tcf(c_82992,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_77937,c_46104]) ).

tcf(c_82993,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77980,c_46104]) ).

tcf(c_82994,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,t))),X0) = pls,
    inference(superposition,[status(thm)],[c_78000,c_46104]) ).

tcf(c_82995,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,one_one_int))),X0) = pls,
    inference(superposition,[status(thm)],[c_78001,c_46104]) ).

tcf(c_82996,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK27(X1,X2))
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_78002,c_46104]) ).

tcf(c_82997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( sP3(X3,X2,X4)
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,X2))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_78003,c_46104]) ).

tcf(c_82998,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK26(iPr_def_14))),X0) = pls,
    inference(superposition,[status(thm)],[c_78196,c_46104]) ).

tcf(c_82999,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X1),X1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_78442,c_46104]) ).

tcf(c_83000,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(pls),iPr_def_15))),X0) = pls,
    inference(superposition,[status(thm)],[c_78635,c_46104]) ).

tcf(c_83001,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(d22set(X1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_78712,c_46104]) ).

tcf(c_83002,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_79163,c_46104]) ).

tcf(c_83003,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_79216,c_46104]) ).

tcf(c_83004,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),X0) = pls,
    inference(superposition,[status(thm)],[c_79239,c_46104]) ).

tcf(c_83005,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)))),X0) = pls,
    inference(superposition,[status(thm)],[c_79288,c_46104]) ).

tcf(c_83006,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),X1) = pls )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_46104]) ).

tcf(c_83007,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),X1) = pls )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_46104]) ).

tcf(c_83008,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80314,c_46104]) ).

tcf(c_83009,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80313,c_46104]) ).

tcf(c_83010,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X1)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80400,c_46104]) ).

tcf(c_83011,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80503,c_46104]) ).

tcf(c_83012,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_81315,c_46104]) ).

tcf(c_83013,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_81465,c_46104]) ).

tcf(c_83014,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_81519,c_46104]) ).

tcf(c_83015,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,X0)),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_82961,c_76855]) ).

tcf(c_83211,plain,
    ! [X0: $i] : is_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_82909]) ).

tcf(c_83213,plain,
    ! [X0: $i] : is_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),
    inference(superposition,[status(thm)],[c_382,c_82909]) ).

tcf(c_83218,plain,
    is_int(hAPP_int_int(iPr_def_13,m)),
    inference(superposition,[status(thm)],[c_59637,c_82909]) ).

tcf(c_83219,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_82909,c_46104]) ).

tcf(c_83220,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X0)),pls) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_880]) ).

tcf(c_83221,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X0)),one_one_nat) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_608]) ).

tcf(c_83222,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_524]) ).

tcf(c_83223,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_523]) ).

tcf(c_83224,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),X0)) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_347]) ).

tcf(c_83225,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),one_one_int) = hAPP_int_int(times_times_int(X0),X0),
    inference(superposition,[status(thm)],[c_82909,c_346]) ).

tcf(c_83260,plain,
    is_int(sK30(d22set(pls))),
    inference(superposition,[status(thm)],[c_76445,c_81401]) ).

tcf(c_83261,plain,
    is_int(sK30(d22set(min))),
    inference(superposition,[status(thm)],[c_76445,c_81402]) ).

tcf(c_83266,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_82918]) ).

tcf(c_83267,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_82918]) ).

tcf(c_83270,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_82918]) ).

tcf(c_83271,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_82918]) ).

tcf(c_83272,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_82918]) ).

tcf(c_83273,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_82918]) ).

tcf(c_83274,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_82918]) ).

tcf(c_83275,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(times_times_int(X0),X0) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_83272,c_83222]) ).

tcf(c_83456,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_82919]) ).

tcf(c_83457,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_82919]) ).

tcf(c_83461,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),number_number_of_int(hAPP_int_int(times_times_int(X1),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_82919]) ).

tcf(c_83462,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_82919]) ).

tcf(c_83465,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_82919]) ).

tcf(c_83466,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_82919]) ).

tcf(c_83476,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),number_number_of_int(hAPP_int_int(times_times_int(X0),X0))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_82913]) ).

tcf(c_83480,plain,
    hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_82913]) ).

tcf(c_83481,plain,
    hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_82913]) ).

tcf(c_83483,plain,
    hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)) = pls,
    inference(superposition,[status(thm)],[c_82861,c_82983]) ).

tcf(c_83484,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X0) = pls,
    inference(superposition,[status(thm)],[c_253,c_82983]) ).

tcf(c_83486,plain,
    hAPP_int_int(div_mod_int(pls),pls) = pls,
    inference(superposition,[status(thm)],[c_1004,c_82983]) ).

tcf(c_83487,plain,
    hAPP_int_int(div_mod_int(sK30(iPr_def_19)),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_76995,c_82983]) ).

tcf(c_83488,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_82983]) ).

tcf(c_83489,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),pls))),
    inference(superposition,[status(thm)],[c_82983,c_76662]) ).

tcf(c_83491,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),pls),X0)),
    inference(superposition,[status(thm)],[c_82983,c_1699]) ).

tcf(c_83498,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_83271]) ).

tcf(c_83499,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_83271]) ).

tcf(c_83500,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_83271]) ).

tcf(c_83501,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_83498,c_78498]) ).

tcf(c_83504,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)),
    inference(superposition,[status(thm)],[c_257,c_79918]) ).

tcf(c_83506,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(one_one_int)) = number_number_of_int(hAPP_int_int(iPr_def_12,m)),
    inference(superposition,[status(thm)],[c_76874,c_79918]) ).

tcf(c_83507,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),m))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),m)),
    inference(superposition,[status(thm)],[c_78759,c_79918]) ).

tcf(c_83508,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0)))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_78930,c_79918]) ).

tcf(c_83509,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_13,iPr_def_14))) = number_number_of_int(hAPP_int_int(iPr_def_13,iPr_def_15)),
    inference(superposition,[status(thm)],[c_78938,c_79918]) ).

tcf(c_83510,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(m)) = number_number_of_int(hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79190,c_79918]) ).

tcf(c_83511,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0)))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),
    inference(superposition,[status(thm)],[c_79161,c_79918]) ).

tcf(c_83512,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14)))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79901,c_79918]) ).

tcf(c_83513,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14)))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79904,c_79918]) ).

tcf(c_83514,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_80530]) ).

tcf(c_83515,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_80528]) ).

tcf(c_83516,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_80527]) ).

tcf(c_83517,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_80428]) ).

tcf(c_83518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_80427]) ).

tcf(c_83519,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_80425]) ).

tcf(c_83520,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_80424]) ).

tcf(c_83521,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_82021]) ).

tcf(c_83522,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79918,c_81465]) ).

tcf(c_83523,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79918,c_81315]) ).

tcf(c_83524,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_79918,c_879]) ).

tcf(c_83525,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79918,c_80314]) ).

tcf(c_83526,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79918,c_80313]) ).

tcf(c_83527,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_80257]) ).

tcf(c_83528,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_79918,c_388]) ).

tcf(c_83529,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79918,c_79563]) ).

tcf(c_83530,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79918,c_79579]) ).

tcf(c_83531,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_79918,c_79562]) ).

tcf(c_83532,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_79918,c_382]) ).

tcf(c_83533,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(plus_plus_int(m),X0)) ),
    inference(superposition,[status(thm)],[c_79918,c_58]) ).

tcf(c_83534,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79918,c_879]) ).

tcf(c_83535,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79918,c_388]) ).

tcf(c_83536,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79918,c_79563]) ).

tcf(c_83537,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79918,c_382]) ).

tcf(c_83538,plain,
    hAPP_int_int(plus_plus_int(number_number_of_int(m)),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(m),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_79957]) ).

tcf(c_83539,plain,
    number_number_of_int(hAPP_int_int(iPr_def_13,iPr_def_14)) = hAPP_int_int(iPr_def_13,iPr_def_14),
    inference(light_normalisation,[status(thm)],[c_83510,c_76402,c_79190]) ).

tcf(c_83540,plain,
    hAPP_int_int(plus_plus_int(m),one_one_int) = number_number_of_int(hAPP_int_int(iPr_def_12,m)),
    inference(light_normalisation,[status(thm)],[c_83506,c_76393]) ).

tcf(c_83581,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(one_one_int),X0)) = one_one_int,
    inference(superposition,[status(thm)],[c_49,c_46106]) ).

tcf(c_83582,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(pls),X0)) = pls,
    inference(superposition,[status(thm)],[c_57,c_46106]) ).

tcf(c_83583,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(undefined_int(int)),X0)) = undefined_int(int),
    inference(superposition,[status(thm)],[c_51,c_46106]) ).

tcf(c_83584,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(multInv(X0,X1)),X2)) = multInv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_52,c_46106]) ).

tcf(c_83585,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(zfact(X0)),X1)) = zfact(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_53,c_46106]) ).

tcf(c_83586,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X1),X1)),X0)) = hAPP_int_int(plus_plus_int(X1),X1),
    inference(superposition,[status(thm)],[c_79191,c_46106]) ).

tcf(c_83587,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(min),X0)) = min,
    inference(superposition,[status(thm)],[c_56,c_46106]) ).

tcf(c_83588,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),X1)) = number_number_of_int(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_58,c_46106]) ).

tcf(c_83589,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(legendre(X0,X1)),X2)) = legendre(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_59,c_46106]) ).

tcf(c_83590,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X1)),X0)) = twoSqu1241645765sum2sq(X1),
    inference(superposition,[status(thm)],[c_61,c_46106]) ).

tcf(c_83591,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(inv(X0,X1)),X2)) = inv(X0,X1) )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_62,c_46106]) ).

tcf(c_83592,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(X2,X0)),X1)) = hAPP_int_int(X2,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_65,c_46106]) ).

tcf(c_83593,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_nat_int(X1,X2)),X0)) = hAPP_nat_int(X1,X2),
    inference(superposition,[status(thm)],[c_67,c_46106]) ).

tcf(c_83594,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(m),X0)) = m,
    inference(superposition,[status(thm)],[c_70,c_46106]) ).

tcf(c_83595,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(s1),X0)) = s1,
    inference(superposition,[status(thm)],[c_71,c_46106]) ).

tcf(c_83596,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(s),X0)) = s,
    inference(superposition,[status(thm)],[c_72,c_46106]) ).

tcf(c_83597,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(t),X0)) = t,
    inference(superposition,[status(thm)],[c_73,c_46106]) ).

tcf(c_83598,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK9),X0)) = sK9,
    inference(superposition,[status(thm)],[c_113,c_46106]) ).

tcf(c_83599,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK10),X0)) = sK10,
    inference(superposition,[status(thm)],[c_451,c_46106]) ).

tcf(c_83600,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK11),X0)) = sK11,
    inference(superposition,[status(thm)],[c_459,c_46106]) ).

tcf(c_83601,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK13),X0)) = sK13,
    inference(superposition,[status(thm)],[c_735,c_46106]) ).

tcf(c_83602,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(quadRes(X1)))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK15(X1,X2)),X0)) = sK15(X1,X2) ) ),
    inference(superposition,[status(thm)],[c_77479,c_46106]) ).

tcf(c_83603,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK22(X0)),X1)) = sK22(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77826,c_46106]) ).

tcf(c_83604,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(twoSqu1154269391sum2sq))
      | ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK23(X0)),X1)) = sK23(X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_77975,c_46106]) ).

tcf(c_83605,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,X2)),X0)) = sK27(X1,X2) ) ),
    inference(superposition,[status(thm)],[c_78002,c_46106]) ).

tcf(c_83606,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),X2)),X1)) = hAPP_int_int(times_times_int(X0),X2) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76863,c_46106]) ).

tcf(c_83607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X1,X2,X3)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK38(X1,X2,X3)),X0)) = sK38(X1,X2,X3) ) ),
    inference(superposition,[status(thm)],[c_1651,c_46106]) ).

tcf(c_83608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP3(X1,X2,X3)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK39(X1,X2,X3)),X0)) = sK39(X1,X2,X3) ) ),
    inference(superposition,[status(thm)],[c_1652,c_46106]) ).

tcf(c_83611,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(iPr_def_14),X0)) = iPr_def_14,
    inference(superposition,[status(thm)],[c_76346,c_46106]) ).

tcf(c_83612,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(iPr_def_15),X0)) = iPr_def_15,
    inference(superposition,[status(thm)],[c_76347,c_46106]) ).

tcf(c_83613,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(iPr_def_16),X0)) = iPr_def_16,
    inference(superposition,[status(thm)],[c_76348,c_46106]) ).

tcf(c_83614,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(iPr_def_17),X0)) = iPr_def_17,
    inference(superposition,[status(thm)],[c_76349,c_46106]) ).

tcf(c_83615,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(iPr_def_18),X0)) = iPr_def_18,
    inference(superposition,[status(thm)],[c_76350,c_46106]) ).

tcf(c_83616,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76385,c_46106]) ).

tcf(c_83617,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,pls))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_76383,c_46106]) ).

tcf(c_83618,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,min)),
    inference(superposition,[status(thm)],[c_76382,c_46106]) ).

tcf(c_83619,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,pls)),
    inference(superposition,[status(thm)],[c_76384,c_46106]) ).

tcf(c_83620,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),X1)) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76776,c_46106]) ).

tcf(c_83621,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X2)),X1)) = hAPP_int_int(plus_plus_int(X0),X2) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_76880,c_46106]) ).

tcf(c_83622,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X1)),X0)) = hAPP_int_int(iPr_def_13,X1),
    inference(superposition,[status(thm)],[c_77054,c_46106]) ).

tcf(c_83623,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(cOMBC_int_int_bool(ord_less_int,pls))),X0)) = sK30(cOMBC_int_int_bool(ord_less_int,pls)),
    inference(superposition,[status(thm)],[c_77703,c_46106]) ).

tcf(c_83624,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),X0)) = sK22(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77831,c_46106]) ).

tcf(c_83625,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X1)),X0)) = hAPP_int_int(iPr_def_12,X1),
    inference(superposition,[status(thm)],[c_77937,c_46106]) ).

tcf(c_83626,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),X0)) = sK23(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_77980,c_46106]) ).

tcf(c_83627,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,t)),X0)) = sK27(X1,t),
    inference(superposition,[status(thm)],[c_78000,c_46106]) ).

tcf(c_83628,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,one_one_int)),X0)) = sK27(X1,one_one_int),
    inference(superposition,[status(thm)],[c_78001,c_46106]) ).

tcf(c_83629,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK27(X1,X2))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)) ) ),
    inference(superposition,[status(thm)],[c_78002,c_46106]) ).

tcf(c_83630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( sP3(X3,X2,X4)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,X2)),X0)) = sK27(X1,X2) ) ),
    inference(superposition,[status(thm)],[c_78003,c_46106]) ).

tcf(c_83631,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),X0)) = sK26(iPr_def_14),
    inference(superposition,[status(thm)],[c_78196,c_46106]) ).

tcf(c_83632,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X1),X1))),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_78442,c_46106]) ).

tcf(c_83633,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(pls),iPr_def_15)),X0)) = hAPP_int_int(minus_minus_int(pls),iPr_def_15),
    inference(superposition,[status(thm)],[c_78635,c_46106]) ).

tcf(c_83634,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(d22set(X1))),X0)) = sK30(d22set(X1)),
    inference(superposition,[status(thm)],[c_78712,c_46106]) ).

tcf(c_83635,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X1))),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_79163,c_46106]) ).

tcf(c_83636,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_14),X1)),X0)) = hAPP_int_int(times_times_int(iPr_def_14),X1),
    inference(superposition,[status(thm)],[c_79216,c_46106]) ).

tcf(c_83637,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X1),iPr_def_14)),X0)) = hAPP_int_int(times_times_int(X1),iPr_def_14),
    inference(superposition,[status(thm)],[c_79239,c_46106]) ).

tcf(c_83638,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14))),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79288,c_46106]) ).

tcf(c_83639,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_79562,c_46106]) ).

tcf(c_83640,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),X1)) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79579,c_46106]) ).

tcf(c_83641,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_80314,c_46106]) ).

tcf(c_83642,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80313,c_46106]) ).

tcf(c_83643,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X1)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80400,c_46106]) ).

tcf(c_83644,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_80503,c_46106]) ).

tcf(c_83645,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_81315,c_46106]) ).

tcf(c_83646,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81465,c_46106]) ).

tcf(c_83647,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_81519,c_46106]) ).

tcf(c_83648,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X1),X1)),X0)) = hAPP_int_int(times_times_int(X1),X1),
    inference(superposition,[status(thm)],[c_82909,c_46106]) ).

tcf(c_83808,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_78124,c_624]) ).

tcf(c_83809,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_624,c_970]) ).

tcf(c_83810,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real))
    | ~ hBOOL(hAPP_int_bool(iPr_def_19,pls)) ),
    inference(light_normalisation,[status(thm)],[c_83808,c_59643]) ).

tcf(c_83818,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_568,c_625]) ).

tcf(c_83824,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),zero_zero_real))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)) ),
    inference(superposition,[status(thm)],[c_568,c_626]) ).

tcf(c_83826,plain,
    is_int(sK30(d22set(iPr_def_14))),
    inference(superposition,[status(thm)],[c_76445,c_81404]) ).

tcf(c_83827,plain,
    is_int(sK30(d22set(iPr_def_15))),
    inference(superposition,[status(thm)],[c_76445,c_81405]) ).

tcf(c_83828,plain,
    is_int(sK30(d22set(iPr_def_17))),
    inference(superposition,[status(thm)],[c_76445,c_81406]) ).

tcf(c_83830,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_83616]) ).

tcf(c_83834,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_83616,c_79918]) ).

tcf(c_83835,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_83616,c_79931]) ).

tcf(c_83836,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_83834,c_76415]) ).

tcf(c_83837,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_83835,c_76415]) ).

tcf(c_83839,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),iPr_def_11))) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_83270,c_255]) ).

tcf(c_83840,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),pls)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_83839]) ).

tcf(c_83841,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),one_one_int)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_83839]) ).

tcf(c_83842,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X0))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_83839]) ).

tcf(c_83843,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_83840,c_76727]) ).

tcf(c_83844,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_83843,c_78498]) ).

tcf(c_83851,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X1),X1)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_83274]) ).

tcf(c_83852,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_83274]) ).

tcf(c_83855,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_83274]) ).

tcf(c_83859,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),number_number_of_int(hAPP_int_int(times_times_int(X1),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_83274]) ).

tcf(c_83860,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_83274]) ).

tcf(c_83863,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_83274]) ).

tcf(c_83864,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_83274]) ).

tcf(c_83874,plain,
    hBOOL(member_int(one_one_int,zcong(sK30(iPr_def_19),pls))),
    inference(superposition,[status(thm)],[c_83487,c_76662]) ).

tcf(c_83876,plain,
    hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),pls),one_one_int)),
    inference(superposition,[status(thm)],[c_83487,c_1699]) ).

tcf(c_83895,plain,
    twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82935,c_82917]) ).

tcf(c_83898,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(times_times_int(X0),X0))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_82917]) ).

tcf(c_83899,plain,
    hAPP_int_int(iPr_def_12,pls) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_82917]) ).

tcf(c_83902,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_82917]) ).

tcf(c_83903,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_82917]) ).

tcf(c_83906,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),m) = hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_79944,c_83504]) ).

tcf(c_83913,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_1241,c_627]) ).

tcf(c_83914,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_568,c_627]) ).

tcf(c_83944,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79573,c_628]) ).

tcf(c_83945,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79414,c_628]) ).

tcf(c_83946,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79557,c_628]) ).

tcf(c_83947,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_628]) ).

tcf(c_83948,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_79918,c_628]) ).

tcf(c_83949,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79931,c_628]) ).

tcf(c_83950,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_628]) ).

tcf(c_83951,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_80677,c_628]) ).

tcf(c_83952,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_628]) ).

tcf(c_83953,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(number_number_of_int(X0),hAPP_i1948725293t_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_628,c_226]) ).

tcf(c_84012,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79573,c_629]) ).

tcf(c_84013,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79414,c_629]) ).

tcf(c_84014,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79557,c_629]) ).

tcf(c_84015,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_629]) ).

tcf(c_84016,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79918,c_629]) ).

tcf(c_84017,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79931,c_629]) ).

tcf(c_84018,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_629]) ).

tcf(c_84019,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80677,c_629]) ).

tcf(c_84020,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_629]) ).

tcf(c_84074,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_78124,c_630]) ).

tcf(c_84080,plain,
    hBOOL(member_int(m,zcong(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),pls))),
    inference(superposition,[status(thm)],[c_83488,c_76662]) ).

tcf(c_84082,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),pls),m)),
    inference(superposition,[status(thm)],[c_83488,c_1699]) ).

tcf(c_84083,plain,
    hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),pls))),
    inference(superposition,[status(thm)],[c_82861,c_83489]) ).

tcf(c_84084,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),pls))),
    inference(superposition,[status(thm)],[c_253,c_83489]) ).

tcf(c_84086,plain,
    hBOOL(member_int(pls,zcong(pls,pls))),
    inference(superposition,[status(thm)],[c_1004,c_83489]) ).

tcf(c_84091,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),pls),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_83491]) ).

tcf(c_84092,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),pls),X0)),
    inference(superposition,[status(thm)],[c_253,c_83491]) ).

tcf(c_84098,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_83491,c_814]) ).

tcf(c_84099,plain,
    ! [X0: $i] : legendre(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),X0) = pls,
    inference(superposition,[status(thm)],[c_83491,c_940]) ).

tcf(c_84100,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_83491,c_930]) ).

tcf(c_84130,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = pls,
    inference(superposition,[status(thm)],[c_80257,c_83484]) ).

tcf(c_84131,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_80257,c_83484]) ).

tcf(c_84132,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0)))) = pls,
    inference(superposition,[status(thm)],[c_82021,c_83484]) ).

tcf(c_84140,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),sK30(iPr_def_19)))
    | ~ is_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)) ),
    inference(superposition,[status(thm)],[c_83830,c_78137]) ).

tcf(c_84142,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),sK30(iPr_def_19)) != hAPP_int_int(plus_plus_int(X0),X0),
    inference(superposition,[status(thm)],[c_83830,c_76515]) ).

tcf(c_84143,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),sK30(iPr_def_19)) != pls,
    inference(superposition,[status(thm)],[c_83830,c_76368]) ).

tcf(c_84153,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(superposition,[status(thm)],[c_1241,c_631]) ).

tcf(c_84155,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_78124,c_631]) ).

tcf(c_84160,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(light_normalisation,[status(thm)],[c_729,c_59643]) ).

tcf(c_84170,plain,
    ! [X0: $i] :
      ( is_int(sK30(zprime))
      | hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_84160]) ).

tcf(c_84171,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,sK26(X0)))
      | ~ is_int(sK26(X0))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(superposition,[status(thm)],[c_78637,c_84160]) ).

tcf(c_84187,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(dvd_dvd_int,pls)))
      | ( X0 = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_1019]) ).

tcf(c_84203,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1295,c_1332]) ).

tcf(c_84204,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X0) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1299,c_1332]) ).

tcf(c_84207,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0))) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1408,c_1332]) ).

tcf(c_84208,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1409,c_1332]) ).

tcf(c_84209,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),X0) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1694,c_1332]) ).

tcf(c_84210,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(div_mod_nat(X0),X2)) = zero_zero_nat )
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1332]) ).

tcf(c_84263,plain,
    is_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80432,c_82861]) ).

tcf(c_84269,plain,
    is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_79285]) ).

tcf(c_84271,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X1),iPr_def_14))),X0)) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_46106]) ).

tcf(c_84272,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X1),iPr_def_14)))),X0) = pls,
    inference(superposition,[status(thm)],[c_79285,c_46104]) ).

tcf(c_84273,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_880]) ).

tcf(c_84274,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))),one_one_nat) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_608]) ).

tcf(c_84275,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))),pls) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_524]) ).

tcf(c_84276,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_523]) ).

tcf(c_84277,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_347]) ).

tcf(c_84278,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))),one_one_int) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_346]) ).

tcf(c_84279,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),iPr_def_14)),
    inference(superposition,[status(thm)],[c_79285,c_254]) ).

tcf(c_84294,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),number_number_of_int(hAPP_int_int(times_times_int(X0),X0))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_83500]) ).

tcf(c_84298,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_83500]) ).

tcf(c_84299,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_83500]) ).

tcf(c_84302,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls)))),
    inference(superposition,[status(thm)],[c_574,c_83525]) ).

tcf(c_84303,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min)))),
    inference(superposition,[status(thm)],[c_76397,c_83525]) ).

tcf(c_84304,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))),
    inference(superposition,[status(thm)],[c_76393,c_83525]) ).

tcf(c_84305,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int))))),
    inference(superposition,[status(thm)],[c_76395,c_83525]) ).

tcf(c_84306,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))))),
    inference(superposition,[status(thm)],[c_76399,c_83525]) ).

tcf(c_84307,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))))),
    inference(superposition,[status(thm)],[c_76401,c_83525]) ).

tcf(c_84308,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))),
    inference(superposition,[status(thm)],[c_76402,c_83525]) ).

tcf(c_84309,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1)))),
    inference(superposition,[status(thm)],[c_76403,c_83525]) ).

tcf(c_84310,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s)))),
    inference(superposition,[status(thm)],[c_76404,c_83525]) ).

tcf(c_84311,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t)))),
    inference(superposition,[status(thm)],[c_76405,c_83525]) ).

tcf(c_84312,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9)))),
    inference(superposition,[status(thm)],[c_76406,c_83525]) ).

tcf(c_84313,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10)))),
    inference(superposition,[status(thm)],[c_76407,c_83525]) ).

tcf(c_84314,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11)))),
    inference(superposition,[status(thm)],[c_76408,c_83525]) ).

tcf(c_84315,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13)))),
    inference(superposition,[status(thm)],[c_76409,c_83525]) ).

tcf(c_84316,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_76410,c_83525]) ).

tcf(c_84317,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15)))),
    inference(superposition,[status(thm)],[c_76411,c_83525]) ).

tcf(c_84318,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16)))),
    inference(superposition,[status(thm)],[c_76412,c_83525]) ).

tcf(c_84319,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17)))),
    inference(superposition,[status(thm)],[c_76413,c_83525]) ).

tcf(c_84320,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18)))),
    inference(superposition,[status(thm)],[c_76414,c_83525]) ).

tcf(c_84321,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76415,c_83525]) ).

tcf(c_84322,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))),
    inference(superposition,[status(thm)],[c_77366,c_83525]) ).

tcf(c_84323,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))),
    inference(superposition,[status(thm)],[c_78203,c_83525]) ).

tcf(c_84325,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79414,c_83525]) ).

tcf(c_84327,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79437,c_83525]) ).

tcf(c_84328,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79918,c_83525]) ).

tcf(c_84329,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79931,c_83525]) ).

tcf(c_84330,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79957,c_83525]) ).

tcf(c_84331,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80677,c_83525]) ).

tcf(c_84332,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80705,c_83525]) ).

tcf(c_84333,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_83525,c_46106]) ).

tcf(c_84334,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_83525,c_46104]) ).

tcf(c_84337,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83525,c_524]) ).

tcf(c_84339,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83525,c_347]) ).

tcf(c_84340,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83525,c_346]) ).

tcf(c_84341,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83525,c_254]) ).

tcf(c_84342,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(light_normalisation,[status(thm)],[c_84308,c_79190]) ).

tcf(c_84381,plain,
    hAPP_int_int(minus_minus_int(m),number_number_of_int(pls)) = number_number_of_int(m),
    inference(superposition,[status(thm)],[c_77414,c_80664]) ).

tcf(c_84382,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80664,c_83525]) ).

tcf(c_84383,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(m),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80664,c_629]) ).

tcf(c_84384,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_80664,c_628]) ).

tcf(c_84385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_80530]) ).

tcf(c_84386,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_80528]) ).

tcf(c_84387,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_80527]) ).

tcf(c_84388,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_80428]) ).

tcf(c_84389,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_80427]) ).

tcf(c_84390,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_80425]) ).

tcf(c_84391,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_80424]) ).

tcf(c_84392,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_82021]) ).

tcf(c_84393,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80664,c_81465]) ).

tcf(c_84394,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80664,c_81315]) ).

tcf(c_84395,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_80664,c_879]) ).

tcf(c_84396,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80664,c_80314]) ).

tcf(c_84397,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80664,c_80313]) ).

tcf(c_84398,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_80257]) ).

tcf(c_84399,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_80664,c_388]) ).

tcf(c_84400,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80664,c_79563]) ).

tcf(c_84401,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80664,c_79579]) ).

tcf(c_84402,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_80664,c_79562]) ).

tcf(c_84403,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),X1)),
    inference(superposition,[status(thm)],[c_80664,c_382]) ).

tcf(c_84404,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(minus_minus_int(m),X0)) ),
    inference(superposition,[status(thm)],[c_80664,c_58]) ).

tcf(c_84405,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_879]) ).

tcf(c_84406,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_388]) ).

tcf(c_84407,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80664,c_79563]) ).

tcf(c_84408,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_382]) ).

tcf(c_84409,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(m)),sK30(iPr_def_19)) = hAPP_int_int(minus_minus_int(m),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_80705]) ).

tcf(c_84478,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X1))
      | ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_11972,c_1333]) ).

tcf(c_84480,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | ( X0 != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1245,c_1333]) ).

tcf(c_84482,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1))
      | ( X0 != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1289,c_1333]) ).

tcf(c_84483,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X0)),X1))
      | ( X0 != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1290,c_1333]) ).

tcf(c_84486,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(iPr_def_10,X0)),one_one_nat))
      | ( X0 != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_77549,c_1333]) ).

tcf(c_84510,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X1),hAPP_nat_nat(div_mod_nat(X0),X2)) = X1 )
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1693]) ).

tcf(c_84511,plain,
    hAPP_nat_nat(div_mod_nat(zero_zero_nat),one_one_nat) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_11147,c_1693]) ).

tcf(c_84512,plain,
    hAPP_nat_nat(div_mod_nat(zero_zero_nat),iPr_def_11) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_76735,c_1693]) ).

tcf(c_84520,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(zcong(X0,pls)))
      | ( hAPP_int_int(div_mod_int(X0),X1) = pls ) ),
    inference(superposition,[status(thm)],[c_1563,c_1697]) ).

tcf(c_84522,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(X0),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_829,c_1697]) ).

tcf(c_84526,plain,
    hAPP_int_int(div_mod_int(pls),min) = pls,
    inference(superposition,[status(thm)],[c_80621,c_1697]) ).

tcf(c_84527,plain,
    hAPP_int_int(div_mod_int(iPr_def_17),iPr_def_16) = pls,
    inference(superposition,[status(thm)],[c_81088,c_1697]) ).

tcf(c_84528,plain,
    hAPP_int_int(div_mod_int(iPr_def_17),m) = pls,
    inference(superposition,[status(thm)],[c_81089,c_1697]) ).

tcf(c_84573,plain,
    ! [X0: $i] : hBOOL(member_int(one_one_int,zcong(X0,pls))),
    inference(superposition,[status(thm)],[c_84522,c_76662]) ).

tcf(c_84588,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14) != one_one_int,
    inference(superposition,[status(thm)],[c_79150,c_79312]) ).

tcf(c_84591,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_46106]) ).

tcf(c_84592,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_84321,c_46104]) ).

tcf(c_84593,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_880]) ).

tcf(c_84594,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_608]) ).

tcf(c_84595,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_524]) ).

tcf(c_84596,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_523]) ).

tcf(c_84597,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_347]) ).

tcf(c_84598,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_346]) ).

tcf(c_84599,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84321,c_254]) ).

tcf(c_84652,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),pls)))),
    inference(superposition,[status(thm)],[c_574,c_84396]) ).

tcf(c_84653,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),min)))),
    inference(superposition,[status(thm)],[c_76397,c_84396]) ).

tcf(c_84654,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),one_one_int)))),
    inference(superposition,[status(thm)],[c_76393,c_84396]) ).

tcf(c_84655,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),undefined_int(int))))),
    inference(superposition,[status(thm)],[c_76395,c_84396]) ).

tcf(c_84656,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0))))),
    inference(superposition,[status(thm)],[c_76399,c_84396]) ).

tcf(c_84657,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1))))),
    inference(superposition,[status(thm)],[c_76401,c_84396]) ).

tcf(c_84658,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),m)))),
    inference(superposition,[status(thm)],[c_76402,c_84396]) ).

tcf(c_84659,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),s1)))),
    inference(superposition,[status(thm)],[c_76403,c_84396]) ).

tcf(c_84660,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),s)))),
    inference(superposition,[status(thm)],[c_76404,c_84396]) ).

tcf(c_84661,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),t)))),
    inference(superposition,[status(thm)],[c_76405,c_84396]) ).

tcf(c_84662,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK9)))),
    inference(superposition,[status(thm)],[c_76406,c_84396]) ).

tcf(c_84663,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK10)))),
    inference(superposition,[status(thm)],[c_76407,c_84396]) ).

tcf(c_84664,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK11)))),
    inference(superposition,[status(thm)],[c_76408,c_84396]) ).

tcf(c_84665,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK13)))),
    inference(superposition,[status(thm)],[c_76409,c_84396]) ).

tcf(c_84666,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_76410,c_84396]) ).

tcf(c_84667,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),iPr_def_15)))),
    inference(superposition,[status(thm)],[c_76411,c_84396]) ).

tcf(c_84668,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),iPr_def_16)))),
    inference(superposition,[status(thm)],[c_76412,c_84396]) ).

tcf(c_84669,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),iPr_def_17)))),
    inference(superposition,[status(thm)],[c_76413,c_84396]) ).

tcf(c_84670,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),iPr_def_18)))),
    inference(superposition,[status(thm)],[c_76414,c_84396]) ).

tcf(c_84672,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0))))),
    inference(superposition,[status(thm)],[c_77366,c_84396]) ).

tcf(c_84673,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14))))),
    inference(superposition,[status(thm)],[c_78203,c_84396]) ).

tcf(c_84675,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79414,c_84396]) ).

tcf(c_84677,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79437,c_84396]) ).

tcf(c_84678,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79918,c_84396]) ).

tcf(c_84679,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_79931,c_84396]) ).

tcf(c_84680,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79957,c_84396]) ).

tcf(c_84681,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80664,c_84396]) ).

tcf(c_84682,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80677,c_84396]) ).

tcf(c_84683,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80705,c_84396]) ).

tcf(c_84684,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_84396,c_46106]) ).

tcf(c_84685,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_84396,c_46104]) ).

tcf(c_84688,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_84396,c_524]) ).

tcf(c_84690,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_84396,c_347]) ).

tcf(c_84691,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_84396,c_346]) ).

tcf(c_84692,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_84396,c_254]) ).

tcf(c_84732,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),iPr_def_11)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_83008]) ).

tcf(c_84733,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),X1)),X1) = pls,
    inference(superposition,[status(thm)],[c_253,c_83008]) ).

tcf(c_84736,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_83008]) ).

tcf(c_84741,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_574,c_83008]) ).

tcf(c_84742,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76397,c_83008]) ).

tcf(c_84743,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76393,c_83008]) ).

tcf(c_84744,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76395,c_83008]) ).

tcf(c_84746,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X1,X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76401,c_83008]) ).

tcf(c_84747,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76402,c_83008]) ).

tcf(c_84748,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76403,c_83008]) ).

tcf(c_84749,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76404,c_83008]) ).

tcf(c_84750,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76405,c_83008]) ).

tcf(c_84751,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76406,c_83008]) ).

tcf(c_84752,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76407,c_83008]) ).

tcf(c_84753,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76408,c_83008]) ).

tcf(c_84754,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76409,c_83008]) ).

tcf(c_84755,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76410,c_83008]) ).

tcf(c_84756,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76411,c_83008]) ).

tcf(c_84757,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76412,c_83008]) ).

tcf(c_84758,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76413,c_83008]) ).

tcf(c_84759,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76414,c_83008]) ).

tcf(c_84760,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76415,c_83008]) ).

tcf(c_84761,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77366,c_83008]) ).

tcf(c_84762,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78203,c_83008]) ).

tcf(c_84764,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79414,c_83008]) ).

tcf(c_84766,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79437,c_83008]) ).

tcf(c_84768,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79931,c_83008]) ).

tcf(c_84769,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79957,c_83008]) ).

tcf(c_84773,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),pls))),
    inference(superposition,[status(thm)],[c_83008,c_76662]) ).

tcf(c_84775,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),pls),X0)),
    inference(superposition,[status(thm)],[c_83008,c_1698]) ).

tcf(c_84777,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84759,c_80284]) ).

tcf(c_84778,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84758,c_80283]) ).

tcf(c_84779,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84757,c_80282]) ).

tcf(c_84780,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84756,c_80281]) ).

tcf(c_84781,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84755,c_80280]) ).

tcf(c_84782,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84754,c_80279]) ).

tcf(c_84783,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84753,c_80278]) ).

tcf(c_84784,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84752,c_80277]) ).

tcf(c_84785,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84751,c_80276]) ).

tcf(c_84786,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84750,c_80275]) ).

tcf(c_84787,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84749,c_80274]) ).

tcf(c_84788,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84748,c_80273]) ).

tcf(c_84789,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84743,c_80316]) ).

tcf(c_84790,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84742,c_80270]) ).

tcf(c_84791,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84741,c_80269]) ).

tcf(c_84899,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),iPr_def_11)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_83009]) ).

tcf(c_84900,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),X1)),X1) = pls,
    inference(superposition,[status(thm)],[c_253,c_83009]) ).

tcf(c_84903,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_80428,c_83009]) ).

tcf(c_84904,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_83009]) ).

tcf(c_84910,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76393,c_83009]) ).

tcf(c_84911,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76395,c_83009]) ).

tcf(c_84913,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X1,X2)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76401,c_83009]) ).

tcf(c_84914,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76402,c_83009]) ).

tcf(c_84928,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X1)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77366,c_83009]) ).

tcf(c_84929,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78203,c_83009]) ).

tcf(c_84931,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79414,c_83009]) ).

tcf(c_84933,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79437,c_83009]) ).

tcf(c_84934,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79918,c_83009]) ).

tcf(c_84935,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79931,c_83009]) ).

tcf(c_84936,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79957,c_83009]) ).

tcf(c_84937,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80664,c_83009]) ).

tcf(c_84938,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80677,c_83009]) ).

tcf(c_84939,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80705,c_83009]) ).

tcf(c_84940,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),pls))),
    inference(superposition,[status(thm)],[c_83009,c_76662]) ).

tcf(c_84942,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),pls),X0)),
    inference(superposition,[status(thm)],[c_83009,c_1698]) ).

tcf(c_84944,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_84914,c_59637]) ).

tcf(c_84988,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))),
    inference(superposition,[status(thm)],[c_80692,c_84396]) ).

tcf(c_84989,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))),
    inference(superposition,[status(thm)],[c_80692,c_83525]) ).

tcf(c_84990,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_629]) ).

tcf(c_84991,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_628]) ).

tcf(c_84992,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_80530]) ).

tcf(c_84993,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_80528]) ).

tcf(c_84994,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_80527]) ).

tcf(c_84995,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_80428]) ).

tcf(c_84996,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_80427]) ).

tcf(c_84997,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_80425]) ).

tcf(c_84998,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_80424]) ).

tcf(c_84999,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_82021]) ).

tcf(c_85000,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80692,c_81465]) ).

tcf(c_85001,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))),
    inference(superposition,[status(thm)],[c_80692,c_81315]) ).

tcf(c_85002,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_80692,c_879]) ).

tcf(c_85003,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),
    inference(superposition,[status(thm)],[c_80692,c_80314]) ).

tcf(c_85004,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80692,c_80313]) ).

tcf(c_85005,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_80257]) ).

tcf(c_85006,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_80692,c_388]) ).

tcf(c_85007,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80692,c_79563]) ).

tcf(c_85008,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80692,c_79579]) ).

tcf(c_85009,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_79562]) ).

tcf(c_85010,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_80692,c_382]) ).

tcf(c_85011,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),m)) ),
    inference(superposition,[status(thm)],[c_80692,c_58]) ).

tcf(c_85012,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80692,c_83009]) ).

tcf(c_85013,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80692,c_83008]) ).

tcf(c_85014,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(X1),m))),
    inference(superposition,[status(thm)],[c_80692,c_879]) ).

tcf(c_85015,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(X1),m))),
    inference(superposition,[status(thm)],[c_80692,c_388]) ).

tcf(c_85016,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_80692,c_79563]) ).

tcf(c_85017,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),m))),
    inference(superposition,[status(thm)],[c_80692,c_382]) ).

tcf(c_85018,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(m)),m) = hAPP_int_int(minus_minus_int(m),number_number_of_int(m)),
    inference(superposition,[status(thm)],[c_80692,c_80664]) ).

tcf(c_85019,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(sK30(iPr_def_19))),m) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(m)),
    inference(superposition,[status(thm)],[c_80692,c_80677]) ).

tcf(c_85119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_bool_bool(hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)),hAPP_int_bool(X3,X2)) = hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(X0,X1),X3),X2),
    inference(superposition,[status(thm)],[c_1722,c_1721]) ).

tcf(c_85120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_bool_bool(hAPP_i68813070l_bool(X0,X1),hAPP_int_bool(hAPP_i1948725293t_bool(X2,X1),X3)) = hAPP_int_bool(cOMBS_int_bool_bool(X0,cOMBC_int_int_bool(X2,X3)),X1),
    inference(superposition,[status(thm)],[c_1720,c_1721]) ).

tcf(c_85121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_bool_bool(hAPP_i68813070l_bool(X0,X1),hAPP_int_bool(cOMBC_int_int_bool(X2,X1),X3)) = hAPP_int_bool(cOMBS_int_bool_bool(X0,hAPP_i1948725293t_bool(X2,X3)),X1),
    inference(superposition,[status(thm)],[c_1720,c_1721]) ).

tcf(c_85122,plain,
    ! [X0: $i] : hAPP_bool_bool(hAPP_i68813070l_bool(X0,t),iPr_def_20) = hAPP_int_bool(cOMBS_int_bool_bool(X0,iPr_def_19),t),
    inference(superposition,[status(thm)],[c_59644,c_1721]) ).

tcf(c_85131,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)) = one_one_int,
    inference(light_normalisation,[status(thm)],[c_14881,c_59634,c_59635,c_76397]) ).

tcf(c_85132,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X0),iPr_def_11)) = one_one_int,
    inference(superposition,[status(thm)],[c_1309,c_85131]) ).

tcf(c_85134,plain,
    hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int,
    inference(superposition,[status(thm)],[c_1413,c_85131]) ).

tcf(c_85135,plain,
    hAPP_nat_int(power_power_int(min),zero_zero_nat) = one_one_int,
    inference(superposition,[status(thm)],[c_1337,c_85131]) ).

tcf(c_85145,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)) = one_one_real,
    inference(light_normalisation,[status(thm)],[c_14882,c_59634,c_59635]) ).

tcf(c_85146,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(X0),iPr_def_11)) = one_one_real,
    inference(superposition,[status(thm)],[c_1309,c_85145]) ).

tcf(c_85148,plain,
    hAPP_nat_real(power_power_real(number267125858f_real(min)),iPr_def_11) = one_one_real,
    inference(superposition,[status(thm)],[c_1413,c_85145]) ).

tcf(c_85149,plain,
    hAPP_nat_real(power_power_real(number267125858f_real(min)),zero_zero_nat) = one_one_real,
    inference(superposition,[status(thm)],[c_1337,c_85145]) ).

tcf(c_85161,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(s),s)),min) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(light_normalisation,[status(thm)],[c_16379,c_76397]) ).

tcf(c_85162,plain,
    ( is_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))
    | ~ is_int(min) ),
    inference(superposition,[status(thm)],[c_85161,c_65]) ).

tcf(c_85166,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14) != iPr_def_15,
    inference(superposition,[status(thm)],[c_79150,c_79551]) ).

tcf(c_85175,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14) != min,
    inference(superposition,[status(thm)],[c_79150,c_80165]) ).

tcf(c_85179,plain,
    hBOOL(hAPP_int_bool(zcong(m,pls),one_one_int)),
    inference(superposition,[status(thm)],[c_76934,c_81086]) ).

tcf(c_85180,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_81086]) ).

tcf(c_85181,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),pls),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_81086]) ).

tcf(c_85182,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(iPr_def_13,X0),pls))),
    inference(superposition,[status(thm)],[c_81086,c_226]) ).

tcf(c_85183,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,X0)),X0)),
    inference(superposition,[status(thm)],[c_81086,c_814]) ).

tcf(c_85185,plain,
    ! [X0: $i] : legendre(hAPP_int_int(iPr_def_13,X0),X0) = pls,
    inference(superposition,[status(thm)],[c_81086,c_940]) ).

tcf(c_85187,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_85180,c_79321]) ).

tcf(c_85193,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(pls),m)))),
    inference(superposition,[status(thm)],[c_574,c_85003]) ).

tcf(c_85194,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(min),m)))),
    inference(superposition,[status(thm)],[c_76397,c_85003]) ).

tcf(c_85195,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(one_one_int),m)))),
    inference(superposition,[status(thm)],[c_76393,c_85003]) ).

tcf(c_85196,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(undefined_int(int)),m)))),
    inference(superposition,[status(thm)],[c_76395,c_85003]) ).

tcf(c_85197,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),m)))),
    inference(superposition,[status(thm)],[c_76399,c_85003]) ).

tcf(c_85198,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),m)))),
    inference(superposition,[status(thm)],[c_76401,c_85003]) ).

tcf(c_85200,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(s1),m)))),
    inference(superposition,[status(thm)],[c_76403,c_85003]) ).

tcf(c_85201,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(s),m)))),
    inference(superposition,[status(thm)],[c_76404,c_85003]) ).

tcf(c_85202,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(t),m)))),
    inference(superposition,[status(thm)],[c_76405,c_85003]) ).

tcf(c_85203,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK9),m)))),
    inference(superposition,[status(thm)],[c_76406,c_85003]) ).

tcf(c_85204,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK10),m)))),
    inference(superposition,[status(thm)],[c_76407,c_85003]) ).

tcf(c_85205,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK11),m)))),
    inference(superposition,[status(thm)],[c_76408,c_85003]) ).

tcf(c_85206,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK13),m)))),
    inference(superposition,[status(thm)],[c_76409,c_85003]) ).

tcf(c_85207,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_14),m)))),
    inference(superposition,[status(thm)],[c_76410,c_85003]) ).

tcf(c_85208,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_15),m)))),
    inference(superposition,[status(thm)],[c_76411,c_85003]) ).

tcf(c_85209,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_16),m)))),
    inference(superposition,[status(thm)],[c_76412,c_85003]) ).

tcf(c_85210,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_17),m)))),
    inference(superposition,[status(thm)],[c_76413,c_85003]) ).

tcf(c_85211,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(iPr_def_18),m)))),
    inference(superposition,[status(thm)],[c_76414,c_85003]) ).

tcf(c_85213,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),m)))),
    inference(superposition,[status(thm)],[c_77366,c_85003]) ).

tcf(c_85214,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),m)))),
    inference(superposition,[status(thm)],[c_78203,c_85003]) ).

tcf(c_85216,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),m)))),
    inference(superposition,[status(thm)],[c_79414,c_85003]) ).

tcf(c_85218,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_79437,c_85003]) ).

tcf(c_85219,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),m)))),
    inference(superposition,[status(thm)],[c_79918,c_85003]) ).

tcf(c_85220,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),m)))),
    inference(superposition,[status(thm)],[c_79931,c_85003]) ).

tcf(c_85221,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_79957,c_85003]) ).

tcf(c_85222,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),m)))),
    inference(superposition,[status(thm)],[c_80664,c_85003]) ).

tcf(c_85223,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),m)))),
    inference(superposition,[status(thm)],[c_80677,c_85003]) ).

tcf(c_85224,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),m)))),
    inference(superposition,[status(thm)],[c_80692,c_85003]) ).

tcf(c_85225,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_80705,c_85003]) ).

tcf(c_85226,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))),
    inference(superposition,[status(thm)],[c_85003,c_46106]) ).

tcf(c_85230,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_85003,c_524]) ).

tcf(c_85232,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_85003,c_347]) ).

tcf(c_85233,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_85003,c_346]) ).

tcf(c_85234,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_85003,c_254]) ).

tcf(c_85345,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(demodulation,[status(thm)],[c_84760,c_82861]) ).

tcf(c_85346,plain,
    hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),iPr_def_11)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_85345]) ).

tcf(c_85347,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),X0) = pls,
    inference(superposition,[status(thm)],[c_253,c_85345]) ).

tcf(c_85350,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_85345]) ).

tcf(c_85351,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls))),
    inference(superposition,[status(thm)],[c_85345,c_76662]) ).

tcf(c_85353,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls),X0)),
    inference(superposition,[status(thm)],[c_85345,c_1698]) ).

tcf(c_85362,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(superposition,[status(thm)],[c_574,c_80531]) ).

tcf(c_85363,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76397,c_80531]) ).

tcf(c_85364,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_80531]) ).

tcf(c_85368,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)),
    inference(superposition,[status(thm)],[c_76402,c_80531]) ).

tcf(c_85369,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_80531]) ).

tcf(c_85370,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)),
    inference(superposition,[status(thm)],[c_76404,c_80531]) ).

tcf(c_85371,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)),
    inference(superposition,[status(thm)],[c_76405,c_80531]) ).

tcf(c_85372,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_80531]) ).

tcf(c_85373,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_80531]) ).

tcf(c_85374,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_80531]) ).

tcf(c_85375,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_80531]) ).

tcf(c_85376,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_80531]) ).

tcf(c_85377,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_80531]) ).

tcf(c_85378,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_80531]) ).

tcf(c_85379,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_80531]) ).

tcf(c_85380,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_80531]) ).

tcf(c_85396,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80531,c_1042]) ).

tcf(c_85397,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80531,c_833]) ).

tcf(c_85399,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_80531,c_76535]) ).

tcf(c_85400,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80531,c_76498]) ).

tcf(c_85401,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80531,c_1045]) ).

tcf(c_85402,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_80531,c_833]) ).

tcf(c_85403,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_80531,c_83008]) ).

tcf(c_85470,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_59636,c_83641]) ).

tcf(c_85476,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(superposition,[status(thm)],[c_574,c_83641]) ).

tcf(c_85477,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76397,c_83641]) ).

tcf(c_85478,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_83641]) ).

tcf(c_85479,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_83641]) ).

tcf(c_85481,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X1,X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_83641]) ).

tcf(c_85482,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),m)),
    inference(superposition,[status(thm)],[c_76402,c_83641]) ).

tcf(c_85483,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_83641]) ).

tcf(c_85484,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),s)),
    inference(superposition,[status(thm)],[c_76404,c_83641]) ).

tcf(c_85485,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),t)),
    inference(superposition,[status(thm)],[c_76405,c_83641]) ).

tcf(c_85486,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_83641]) ).

tcf(c_85487,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_83641]) ).

tcf(c_85488,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_83641]) ).

tcf(c_85489,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_83641]) ).

tcf(c_85490,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_83641]) ).

tcf(c_85491,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_83641]) ).

tcf(c_85492,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_83641]) ).

tcf(c_85493,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_83641]) ).

tcf(c_85494,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_83641]) ).

tcf(c_85495,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_83641]) ).

tcf(c_85496,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_83641]) ).

tcf(c_85497,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_83641]) ).

tcf(c_85499,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79414,c_83641]) ).

tcf(c_85501,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_83641]) ).

tcf(c_85503,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79931,c_83641]) ).

tcf(c_85504,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79957,c_83641]) ).

tcf(c_85510,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_83641,c_76880]) ).

tcf(c_85511,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),m))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83641,c_79918]) ).

tcf(c_85512,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83641,c_79931]) ).

tcf(c_85513,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85494,c_80284]) ).

tcf(c_85514,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85493,c_80283]) ).

tcf(c_85515,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85492,c_80282]) ).

tcf(c_85516,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85491,c_80281]) ).

tcf(c_85517,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85490,c_80280]) ).

tcf(c_85518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85489,c_80279]) ).

tcf(c_85519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85488,c_80278]) ).

tcf(c_85520,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85487,c_80277]) ).

tcf(c_85521,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85486,c_80276]) ).

tcf(c_85522,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(t),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85485,c_80275]) ).

tcf(c_85523,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85484,c_80274]) ).

tcf(c_85524,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(s1),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85483,c_80273]) ).

tcf(c_85525,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_85478,c_80316]) ).

tcf(c_85526,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85477,c_80270]) ).

tcf(c_85527,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85476,c_80269]) ).

tcf(c_85587,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59636,c_83642]) ).

tcf(c_85594,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76393,c_83642]) ).

tcf(c_85595,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76395,c_83642]) ).

tcf(c_85597,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X1,X2)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(X1,X2)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76401,c_83642]) ).

tcf(c_85598,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76402,c_83642]) ).

tcf(c_85612,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X1)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X1)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_77366,c_83642]) ).

tcf(c_85613,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_78203,c_83642]) ).

tcf(c_85615,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79414,c_83642]) ).

tcf(c_85617,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_83642]) ).

tcf(c_85618,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79918,c_83642]) ).

tcf(c_85619,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79931,c_83642]) ).

tcf(c_85620,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79957,c_83642]) ).

tcf(c_85621,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80664,c_83642]) ).

tcf(c_85622,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80677,c_83642]) ).

tcf(c_85623,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80692,c_83642]) ).

tcf(c_85624,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80705,c_83642]) ).

tcf(c_85626,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_83642,c_76880]) ).

tcf(c_85627,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),m))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_83642,c_79918]) ).

tcf(c_85628,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_83642,c_79931]) ).

tcf(c_85629,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_85598,c_59637]) ).

tcf(c_85658,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_85495,c_82861]) ).

tcf(c_85659,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_59636,c_85658]) ).

tcf(c_85662,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_85658,c_79918]) ).

tcf(c_85663,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_85658,c_79931]) ).

tcf(c_85674,plain,
    hAPP_int_int(iPr_def_13,m) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_83501,c_77362]) ).

tcf(c_85679,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_45914]) ).

tcf(c_85680,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),min)) ),
    inference(superposition,[status(thm)],[c_76397,c_45914]) ).

tcf(c_85682,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),undefined_int(int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_76395,c_45914]) ).

tcf(c_85683,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),twoSqu1241645765sum2sq(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),twoSqu1241645765sum2sq(X0))) ),
    inference(superposition,[status(thm)],[c_76399,c_45914]) ).

tcf(c_85684,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(X0,X1))) ),
    inference(superposition,[status(thm)],[c_76401,c_45914]) ).

tcf(c_85685,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_76402,c_45914]) ).

tcf(c_85686,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),s1))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),s1)) ),
    inference(superposition,[status(thm)],[c_76403,c_45914]) ).

tcf(c_85687,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),s))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),s)) ),
    inference(superposition,[status(thm)],[c_76404,c_45914]) ).

tcf(c_85689,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK9))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK9)) ),
    inference(superposition,[status(thm)],[c_76406,c_45914]) ).

tcf(c_85690,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK10))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK10)) ),
    inference(superposition,[status(thm)],[c_76407,c_45914]) ).

tcf(c_85691,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK11))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK11)) ),
    inference(superposition,[status(thm)],[c_76408,c_45914]) ).

tcf(c_85692,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK13))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK13)) ),
    inference(superposition,[status(thm)],[c_76409,c_45914]) ).

tcf(c_85693,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_76410,c_45914]) ).

tcf(c_85694,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_15))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_76411,c_45914]) ).

tcf(c_85695,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_16))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_76412,c_45914]) ).

tcf(c_85696,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_17))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_76413,c_45914]) ).

tcf(c_85697,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_18))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_76414,c_45914]) ).

tcf(c_85698,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK30(iPr_def_19)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_76415,c_45914]) ).

tcf(c_85699,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_13,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_13,X0))) ),
    inference(superposition,[status(thm)],[c_77366,c_45914]) ).

tcf(c_85700,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK26(iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78203,c_45914]) ).

tcf(c_85701,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79573,c_45914]) ).

tcf(c_85702,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79414,c_45914]) ).

tcf(c_85703,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79557,c_45914]) ).

tcf(c_85704,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_45914]) ).

tcf(c_85705,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_79918,c_45914]) ).

tcf(c_85706,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79931,c_45914]) ).

tcf(c_85707,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_45914]) ).

tcf(c_85708,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_80664,c_45914]) ).

tcf(c_85709,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_80677,c_45914]) ).

tcf(c_85710,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_45914]) ).

tcf(c_85711,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_45914]) ).

tcf(c_85712,plain,
    ! [X0: $i] :
      ( ~ hBOOL(member_int(number_number_of_int(X0),d22set(pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45914,c_1579]) ).

tcf(c_85713,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(number_number_of_int(X0),hAPP_i1948725293t_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45914,c_226]) ).

tcf(c_85714,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45914,c_611]) ).

tcf(c_85739,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),min)),
    inference(forward_subsumption_resolution,[status(thm)],[c_85680,c_764]) ).

tcf(c_85740,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)),
    inference(forward_subsumption_resolution,[status(thm)],[c_85679,c_571]) ).

tcf(c_85831,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45918,c_970]) ).

tcf(c_85851,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45950,c_1693]) ).

tcf(c_85852,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),number_number_of_nat(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45950,c_1364]) ).

tcf(c_85860,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_45978]) ).

tcf(c_85861,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),min))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)) ),
    inference(superposition,[status(thm)],[c_76397,c_45978]) ).

tcf(c_85863,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),undefined_int(int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,undefined_int(int)),pls)) ),
    inference(superposition,[status(thm)],[c_76395,c_45978]) ).

tcf(c_85864,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),twoSqu1241645765sum2sq(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,twoSqu1241645765sum2sq(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_76399,c_45978]) ).

tcf(c_85865,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X0,X1)),pls)) ),
    inference(superposition,[status(thm)],[c_76401,c_45978]) ).

tcf(c_85866,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,m),pls)) ),
    inference(superposition,[status(thm)],[c_76402,c_45978]) ).

tcf(c_85867,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),s1))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,s1),pls)) ),
    inference(superposition,[status(thm)],[c_76403,c_45978]) ).

tcf(c_85868,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),s))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,s),pls)) ),
    inference(superposition,[status(thm)],[c_76404,c_45978]) ).

tcf(c_85869,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),t))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,t),pls)) ),
    inference(superposition,[status(thm)],[c_76405,c_45978]) ).

tcf(c_85870,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK9))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK9),pls)) ),
    inference(superposition,[status(thm)],[c_76406,c_45978]) ).

tcf(c_85871,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK10))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK10),pls)) ),
    inference(superposition,[status(thm)],[c_76407,c_45978]) ).

tcf(c_85872,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK11))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK11),pls)) ),
    inference(superposition,[status(thm)],[c_76408,c_45978]) ).

tcf(c_85873,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK13))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK13),pls)) ),
    inference(superposition,[status(thm)],[c_76409,c_45978]) ).

tcf(c_85874,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),pls)) ),
    inference(superposition,[status(thm)],[c_76410,c_45978]) ).

tcf(c_85875,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),iPr_def_15))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_15),pls)) ),
    inference(superposition,[status(thm)],[c_76411,c_45978]) ).

tcf(c_85876,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),iPr_def_16))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_16),pls)) ),
    inference(superposition,[status(thm)],[c_76412,c_45978]) ).

tcf(c_85877,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),iPr_def_17))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_17),pls)) ),
    inference(superposition,[status(thm)],[c_76413,c_45978]) ).

tcf(c_85878,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),iPr_def_18))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_18),pls)) ),
    inference(superposition,[status(thm)],[c_76414,c_45978]) ).

tcf(c_85879,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK30(iPr_def_19)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK30(iPr_def_19)),pls)) ),
    inference(superposition,[status(thm)],[c_76415,c_45978]) ).

tcf(c_85880,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_13,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_13,X0)),pls)) ),
    inference(superposition,[status(thm)],[c_77366,c_45978]) ).

tcf(c_85881,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK26(iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK26(iPr_def_14)),pls)) ),
    inference(superposition,[status(thm)],[c_78203,c_45978]) ).

tcf(c_85882,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79573,c_45978]) ).

tcf(c_85883,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79414,c_45978]) ).

tcf(c_85884,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79557,c_45978]) ).

tcf(c_85885,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79437,c_45978]) ).

tcf(c_85886,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(m),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79918,c_45978]) ).

tcf(c_85887,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79931,c_45978]) ).

tcf(c_85888,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79957,c_45978]) ).

tcf(c_85889,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(m),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_80664,c_45978]) ).

tcf(c_85890,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_80677,c_45978]) ).

tcf(c_85891,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(X0),m)),pls)) ),
    inference(superposition,[status(thm)],[c_80692,c_45978]) ).

tcf(c_85892,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_80705,c_45978]) ).

tcf(c_85893,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(number_number_of_int(X0),cOMBC_int_int_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_45978,c_226]) ).

tcf(c_85920,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),min)),
    inference(forward_subsumption_resolution,[status(thm)],[c_85861,c_774]) ).

tcf(c_85921,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls)),
    inference(forward_subsumption_resolution,[status(thm)],[c_85860,c_114]) ).

tcf(c_86035,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),
    inference(superposition,[status(thm)],[c_1563,c_85739]) ).

tcf(c_86036,plain,
    ! [X0: $i,X1: $i] : sP3(X0,min,X1),
    inference(superposition,[status(thm)],[c_46418,c_85739]) ).

tcf(c_86041,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_82916]) ).

tcf(c_86052,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80431,c_524]) ).

tcf(c_86055,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80431,c_346]) ).

tcf(c_86056,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_80431,c_254]) ).

tcf(c_86059,plain,
    hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),m)),
    inference(superposition,[status(thm)],[c_84082,c_814]) ).

tcf(c_86061,plain,
    legendre(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),m) = pls,
    inference(superposition,[status(thm)],[c_84082,c_940]) ).

tcf(c_86062,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_84082,c_930]) ).

tcf(c_86090,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(pls)) = number_number_of_int(m),
    inference(superposition,[status(thm)],[c_77148,c_83504]) ).

tcf(c_86093,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),m)),pls)) ),
    inference(superposition,[status(thm)],[c_83504,c_45978]) ).

tcf(c_86094,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_83504,c_45914]) ).

tcf(c_86099,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83504,c_629]) ).

tcf(c_86100,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_83504,c_628]) ).

tcf(c_86111,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_83504,c_879]) ).

tcf(c_86115,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_83504,c_388]) ).

tcf(c_86116,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_83504,c_79563]) ).

tcf(c_86117,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83504,c_79579]) ).

tcf(c_86118,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_83504,c_79562]) ).

tcf(c_86119,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)),
    inference(superposition,[status(thm)],[c_83504,c_382]) ).

tcf(c_86120,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),m)) ),
    inference(superposition,[status(thm)],[c_83504,c_58]) ).

tcf(c_86125,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_83504,c_879]) ).

tcf(c_86126,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_83504,c_388]) ).

tcf(c_86127,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_83504,c_79563]) ).

tcf(c_86128,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_83504,c_382]) ).

tcf(c_86129,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(m)) = hAPP_int_int(plus_plus_int(m),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_83504,c_79931]) ).

tcf(c_86133,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m) = hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_86129,c_76402,c_76415]) ).

tcf(c_86185,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),min))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)) ),
    inference(superposition,[status(thm)],[c_76397,c_45982]) ).

tcf(c_86186,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_76393,c_45982]) ).

tcf(c_86187,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),undefined_int(int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,undefined_int(int)),pls)) ),
    inference(superposition,[status(thm)],[c_76395,c_45982]) ).

tcf(c_86188,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_76399,c_45982]) ).

tcf(c_86189,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(X0,X1)),pls)) ),
    inference(superposition,[status(thm)],[c_76401,c_45982]) ).

tcf(c_86190,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),pls)) ),
    inference(superposition,[status(thm)],[c_76402,c_45982]) ).

tcf(c_86191,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),s1))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s1),pls)) ),
    inference(superposition,[status(thm)],[c_76403,c_45982]) ).

tcf(c_86192,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),s))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),pls)) ),
    inference(superposition,[status(thm)],[c_76404,c_45982]) ).

tcf(c_86193,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),t))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),pls)) ),
    inference(superposition,[status(thm)],[c_76405,c_45982]) ).

tcf(c_86194,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK9))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK9),pls)) ),
    inference(superposition,[status(thm)],[c_76406,c_45982]) ).

tcf(c_86195,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK10))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),pls)) ),
    inference(superposition,[status(thm)],[c_76407,c_45982]) ).

tcf(c_86196,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK11))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),pls)) ),
    inference(superposition,[status(thm)],[c_76408,c_45982]) ).

tcf(c_86197,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK13))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK13),pls)) ),
    inference(superposition,[status(thm)],[c_76409,c_45982]) ).

tcf(c_86198,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),pls)) ),
    inference(superposition,[status(thm)],[c_76410,c_45982]) ).

tcf(c_86199,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_15))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),pls)) ),
    inference(superposition,[status(thm)],[c_76411,c_45982]) ).

tcf(c_86200,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_16))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),pls)) ),
    inference(superposition,[status(thm)],[c_76412,c_45982]) ).

tcf(c_86201,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_17))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),pls)) ),
    inference(superposition,[status(thm)],[c_76413,c_45982]) ).

tcf(c_86202,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_18))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),pls)) ),
    inference(superposition,[status(thm)],[c_76414,c_45982]) ).

tcf(c_86203,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK30(iPr_def_19)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),pls)) ),
    inference(superposition,[status(thm)],[c_76415,c_45982]) ).

tcf(c_86204,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_13,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_13,X0)),pls)) ),
    inference(superposition,[status(thm)],[c_77366,c_45982]) ).

tcf(c_86205,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK26(iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26(iPr_def_14)),pls)) ),
    inference(superposition,[status(thm)],[c_78203,c_45982]) ).

tcf(c_86206,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79573,c_45982]) ).

tcf(c_86207,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79414,c_45982]) ).

tcf(c_86208,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79557,c_45982]) ).

tcf(c_86209,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79437,c_45982]) ).

tcf(c_86210,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79918,c_45982]) ).

tcf(c_86211,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_79931,c_45982]) ).

tcf(c_86212,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),m)),pls)) ),
    inference(superposition,[status(thm)],[c_83504,c_45982]) ).

tcf(c_86213,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_79957,c_45982]) ).

tcf(c_86214,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_80664,c_45982]) ).

tcf(c_86215,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_80677,c_45982]) ).

tcf(c_86216,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),m)),pls)) ),
    inference(superposition,[status(thm)],[c_80692,c_45982]) ).

tcf(c_86217,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_80705,c_45982]) ).

tcf(c_86218,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(number_number_of_int(X0),cOMBC_int_int_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_45982,c_226]) ).

tcf(c_86245,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),one_one_int))
    | ~ hBOOL(hAPP_int_bool(iPr_def_19,pls)) ),
    inference(light_normalisation,[status(thm)],[c_86186,c_59643]) ).

tcf(c_86246,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),min)),
    inference(forward_subsumption_resolution,[status(thm)],[c_86185,c_768]) ).

tcf(c_86373,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_46112]) ).

tcf(c_86374,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)),
    inference(superposition,[status(thm)],[c_575,c_46112]) ).

tcf(c_86375,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_45914,c_46112]) ).

tcf(c_86378,plain,
    ! [X0: $i] :
      ( ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X0)) ),
    inference(superposition,[status(thm)],[c_78137,c_46112]) ).

tcf(c_86379,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),iPr_def_14)),
    inference(superposition,[status(thm)],[c_78155,c_46112]) ).

tcf(c_86380,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),iPr_def_15)),
    inference(superposition,[status(thm)],[c_78154,c_46112]) ).

tcf(c_86381,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),iPr_def_17)),
    inference(superposition,[status(thm)],[c_78153,c_46112]) ).

tcf(c_86382,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),pls)),
    inference(superposition,[status(thm)],[c_80152,c_46112]) ).

tcf(c_86383,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_46112]) ).

tcf(c_86384,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59643,c_46112]) ).

tcf(c_86402,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),sK26(X0)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_46196,c_59643]) ).

tcf(c_86409,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(sK26(X0),cOMBC_int_int_bool(dvd_dvd_int,X0)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(superposition,[status(thm)],[c_86402,c_226]) ).

tcf(c_86417,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_568,c_137]) ).

tcf(c_86418,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_78124,c_137]) ).

tcf(c_86420,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_78124,c_137]) ).

tcf(c_86421,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_137,c_970]) ).

tcf(c_86422,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X0)),
    inference(superposition,[status(thm)],[c_137,c_971]) ).

tcf(c_86425,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_86418,c_59643]) ).

tcf(c_86434,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_46106]) ).

tcf(c_86435,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))),X0) = pls,
    inference(superposition,[status(thm)],[c_86035,c_46104]) ).

tcf(c_86436,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_880]) ).

tcf(c_86437,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_608]) ).

tcf(c_86438,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_524]) ).

tcf(c_86439,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_523]) ).

tcf(c_86440,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_347]) ).

tcf(c_86441,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_346]) ).

tcf(c_86442,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))) = sK30(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)),
    inference(superposition,[status(thm)],[c_86035,c_254]) ).

tcf(c_86447,plain,
    ! [X0: $i,X1: $i] : sP3(X0,pls,X1),
    inference(superposition,[status(thm)],[c_46418,c_85740]) ).

tcf(c_86452,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_880]) ).

tcf(c_86453,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_608]) ).

tcf(c_86454,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_524]) ).

tcf(c_86455,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_523]) ).

tcf(c_86456,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_347]) ).

tcf(c_86457,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_346]) ).

tcf(c_86458,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82865,c_254]) ).

tcf(c_86464,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_80257,c_84084]) ).

tcf(c_86465,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),pls))),
    inference(superposition,[status(thm)],[c_80257,c_84084]) ).

tcf(c_86466,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_82021,c_84084]) ).

tcf(c_86476,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80257,c_84092]) ).

tcf(c_86477,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_84092]) ).

tcf(c_86478,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_82021,c_84092]) ).

tcf(c_86480,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X0)),
    inference(superposition,[status(thm)],[c_84092,c_814]) ).

tcf(c_86482,plain,
    ! [X0: $i] : legendre(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),X0) = pls,
    inference(superposition,[status(thm)],[c_84092,c_940]) ).

tcf(c_86483,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_84092,c_930]) ).

tcf(c_86519,plain,
    hBOOL(hAPP_int_bool(zcong(pls,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_84098]) ).

tcf(c_86523,plain,
    hBOOL(hAPP_int_bool(zcong(pls,sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_76995,c_84098]) ).

tcf(c_86525,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(pls,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_84098,c_226]) ).

tcf(c_86528,plain,
    legendre(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19)) = pls,
    inference(superposition,[status(thm)],[c_82861,c_84099]) ).

tcf(c_86531,plain,
    legendre(pls,pls) = pls,
    inference(superposition,[status(thm)],[c_1004,c_84099]) ).

tcf(c_86532,plain,
    legendre(sK30(iPr_def_19),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_76995,c_84099]) ).

tcf(c_86539,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_80433,c_524]) ).

tcf(c_86542,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_80433,c_346]) ).

tcf(c_86543,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_80433,c_254]) ).

tcf(c_86549,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
    inference(superposition,[status(thm)],[c_568,c_138]) ).

tcf(c_86550,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(superposition,[status(thm)],[c_78124,c_138]) ).

tcf(c_86552,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(superposition,[status(thm)],[c_78124,c_138]) ).

tcf(c_86555,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(light_normalisation,[status(thm)],[c_86550,c_59643]) ).

tcf(c_86565,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_169]) ).

tcf(c_86566,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_574,c_169]) ).

tcf(c_86567,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_76397,c_169]) ).

tcf(c_86568,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_76393,c_169]) ).

tcf(c_86569,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,undefined_int(int)),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,undefined_int(int)),X0)) ),
    inference(superposition,[status(thm)],[c_76395,c_169]) ).

tcf(c_86570,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(X0)),X1)) ),
    inference(superposition,[status(thm)],[c_76399,c_169]) ).

tcf(c_86571,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(X0,X1)),number_number_of_int(X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(X0,X1)),X2)) ),
    inference(superposition,[status(thm)],[c_76401,c_169]) ).

tcf(c_86572,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),X0)) ),
    inference(superposition,[status(thm)],[c_76402,c_169]) ).

tcf(c_86573,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s1),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s1),X0)) ),
    inference(superposition,[status(thm)],[c_76403,c_169]) ).

tcf(c_86574,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),X0)) ),
    inference(superposition,[status(thm)],[c_76404,c_169]) ).

tcf(c_86575,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),X0)) ),
    inference(superposition,[status(thm)],[c_76405,c_169]) ).

tcf(c_86576,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK9),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK9),X0)) ),
    inference(superposition,[status(thm)],[c_76406,c_169]) ).

tcf(c_86577,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),X0)) ),
    inference(superposition,[status(thm)],[c_76407,c_169]) ).

tcf(c_86578,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),X0)) ),
    inference(superposition,[status(thm)],[c_76408,c_169]) ).

tcf(c_86579,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK13),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK13),X0)) ),
    inference(superposition,[status(thm)],[c_76409,c_169]) ).

tcf(c_86580,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),X0)) ),
    inference(superposition,[status(thm)],[c_76410,c_169]) ).

tcf(c_86581,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),X0)) ),
    inference(superposition,[status(thm)],[c_76411,c_169]) ).

tcf(c_86582,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),X0)) ),
    inference(superposition,[status(thm)],[c_76412,c_169]) ).

tcf(c_86583,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),X0)) ),
    inference(superposition,[status(thm)],[c_76413,c_169]) ).

tcf(c_86584,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),X0)) ),
    inference(superposition,[status(thm)],[c_76414,c_169]) ).

tcf(c_86585,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_76415,c_169]) ).

tcf(c_86586,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_13,X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_13,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_77366,c_169]) ).

tcf(c_86587,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26(iPr_def_14)),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26(iPr_def_14)),X0)) ),
    inference(superposition,[status(thm)],[c_78203,c_169]) ).

tcf(c_86588,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79573,c_169]) ).

tcf(c_86589,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79414,c_169]) ).

tcf(c_86590,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_79557,c_169]) ).

tcf(c_86591,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_79437,c_169]) ).

tcf(c_86592,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79918,c_169]) ).

tcf(c_86593,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79931,c_169]) ).

tcf(c_86594,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),m)),X1)) ),
    inference(superposition,[status(thm)],[c_83504,c_169]) ).

tcf(c_86595,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_79957,c_169]) ).

tcf(c_86596,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_80664,c_169]) ).

tcf(c_86597,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_80677,c_169]) ).

tcf(c_86598,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),m)),X1)) ),
    inference(superposition,[status(thm)],[c_80692,c_169]) ).

tcf(c_86599,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_80705,c_169]) ).

tcf(c_86600,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_169]) ).

tcf(c_86601,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_76397,c_169]) ).

tcf(c_86602,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76393,c_169]) ).

tcf(c_86603,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),undefined_int(int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_76395,c_169]) ).

tcf(c_86604,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),twoSqu1241645765sum2sq(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),twoSqu1241645765sum2sq(X1))) ),
    inference(superposition,[status(thm)],[c_76399,c_169]) ).

tcf(c_86605,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_nat_int(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_nat_int(X1,X2))) ),
    inference(superposition,[status(thm)],[c_76401,c_169]) ).

tcf(c_86606,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),m))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),m)) ),
    inference(superposition,[status(thm)],[c_76402,c_169]) ).

tcf(c_86607,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),s1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),s1)) ),
    inference(superposition,[status(thm)],[c_76403,c_169]) ).

tcf(c_86608,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),s))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),s)) ),
    inference(superposition,[status(thm)],[c_76404,c_169]) ).

tcf(c_86609,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),t))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),t)) ),
    inference(superposition,[status(thm)],[c_76405,c_169]) ).

tcf(c_86610,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK9))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK9)) ),
    inference(superposition,[status(thm)],[c_76406,c_169]) ).

tcf(c_86611,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK10))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK10)) ),
    inference(superposition,[status(thm)],[c_76407,c_169]) ).

tcf(c_86612,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK11))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK11)) ),
    inference(superposition,[status(thm)],[c_76408,c_169]) ).

tcf(c_86613,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK13))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK13)) ),
    inference(superposition,[status(thm)],[c_76409,c_169]) ).

tcf(c_86614,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_14))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_76410,c_169]) ).

tcf(c_86615,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_15))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_76411,c_169]) ).

tcf(c_86616,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_16))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_76412,c_169]) ).

tcf(c_86617,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_17))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_76413,c_169]) ).

tcf(c_86618,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_18))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_76414,c_169]) ).

tcf(c_86619,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_76415,c_169]) ).

tcf(c_86620,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(iPr_def_13,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_13,X1))) ),
    inference(superposition,[status(thm)],[c_77366,c_169]) ).

tcf(c_86621,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK26(iPr_def_14)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78203,c_169]) ).

tcf(c_86622,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))) ),
    inference(superposition,[status(thm)],[c_79573,c_169]) ).

tcf(c_86623,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))) ),
    inference(superposition,[status(thm)],[c_79414,c_169]) ).

tcf(c_86624,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79557,c_169]) ).

tcf(c_86625,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_169]) ).

tcf(c_86626,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(m),X1))) ),
    inference(superposition,[status(thm)],[c_79918,c_169]) ).

tcf(c_86627,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))) ),
    inference(superposition,[status(thm)],[c_79931,c_169]) ).

tcf(c_86628,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),m))) ),
    inference(superposition,[status(thm)],[c_83504,c_169]) ).

tcf(c_86629,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_169]) ).

tcf(c_86630,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(m),X1))) ),
    inference(superposition,[status(thm)],[c_80664,c_169]) ).

tcf(c_86631,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))) ),
    inference(superposition,[status(thm)],[c_80677,c_169]) ).

tcf(c_86632,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_169]) ).

tcf(c_86633,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_169]) ).

tcf(c_86634,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_169,c_46112]) ).

tcf(c_86635,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(member_int(number_number_of_int(X0),d22set(number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_169,c_1579]) ).

tcf(c_86636,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(number_number_of_int(X1),hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_169,c_226]) ).

tcf(c_86695,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_86568,c_59643]) ).

tcf(c_86978,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_170]) ).

tcf(c_86979,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_1720,c_170]) ).

tcf(c_86980,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_574,c_170]) ).

tcf(c_86981,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76397,c_170]) ).

tcf(c_86982,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76393,c_170]) ).

tcf(c_86983,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,undefined_int(int)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,undefined_int(int)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76395,c_170]) ).

tcf(c_86984,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_76399,c_170]) ).

tcf(c_86985,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(X0,X1)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(X0,X1)),number_number_of_int(X2))) ),
    inference(superposition,[status(thm)],[c_76401,c_170]) ).

tcf(c_86986,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76402,c_170]) ).

tcf(c_86987,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s1),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76403,c_170]) ).

tcf(c_86988,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76404,c_170]) ).

tcf(c_86989,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76405,c_170]) ).

tcf(c_86990,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK9),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK9),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76406,c_170]) ).

tcf(c_86991,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK10),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76407,c_170]) ).

tcf(c_86992,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK11),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76408,c_170]) ).

tcf(c_86993,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK13),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK13),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76409,c_170]) ).

tcf(c_86994,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76410,c_170]) ).

tcf(c_86995,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76411,c_170]) ).

tcf(c_86996,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76412,c_170]) ).

tcf(c_86997,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76413,c_170]) ).

tcf(c_86998,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76414,c_170]) ).

tcf(c_86999,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_76415,c_170]) ).

tcf(c_87000,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_13,X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_13,X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_77366,c_170]) ).

tcf(c_87001,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26(iPr_def_14)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26(iPr_def_14)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_78203,c_170]) ).

tcf(c_87002,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79573,c_170]) ).

tcf(c_87003,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79414,c_170]) ).

tcf(c_87004,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79557,c_170]) ).

tcf(c_87005,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79437,c_170]) ).

tcf(c_87006,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79918,c_170]) ).

tcf(c_87007,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79931,c_170]) ).

tcf(c_87008,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),m)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_83504,c_170]) ).

tcf(c_87009,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_79957,c_170]) ).

tcf(c_87010,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_80664,c_170]) ).

tcf(c_87011,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_80677,c_170]) ).

tcf(c_87012,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),m)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_80692,c_170]) ).

tcf(c_87013,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_80705,c_170]) ).

tcf(c_87014,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_170]) ).

tcf(c_87015,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),min)) ),
    inference(superposition,[status(thm)],[c_76397,c_170]) ).

tcf(c_87016,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76393,c_170]) ).

tcf(c_87017,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),undefined_int(int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_76395,c_170]) ).

tcf(c_87018,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),twoSqu1241645765sum2sq(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),twoSqu1241645765sum2sq(X1))) ),
    inference(superposition,[status(thm)],[c_76399,c_170]) ).

tcf(c_87019,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_nat_int(X1,X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_nat_int(X1,X2))) ),
    inference(superposition,[status(thm)],[c_76401,c_170]) ).

tcf(c_87020,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),m))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),m)) ),
    inference(superposition,[status(thm)],[c_76402,c_170]) ).

tcf(c_87021,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),s1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),s1)) ),
    inference(superposition,[status(thm)],[c_76403,c_170]) ).

tcf(c_87022,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),s))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),s)) ),
    inference(superposition,[status(thm)],[c_76404,c_170]) ).

tcf(c_87023,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),t))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),t)) ),
    inference(superposition,[status(thm)],[c_76405,c_170]) ).

tcf(c_87024,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK9))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK9)) ),
    inference(superposition,[status(thm)],[c_76406,c_170]) ).

tcf(c_87025,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK10))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK10)) ),
    inference(superposition,[status(thm)],[c_76407,c_170]) ).

tcf(c_87026,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK11))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK11)) ),
    inference(superposition,[status(thm)],[c_76408,c_170]) ).

tcf(c_87027,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK13))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK13)) ),
    inference(superposition,[status(thm)],[c_76409,c_170]) ).

tcf(c_87028,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_14))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_76410,c_170]) ).

tcf(c_87029,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_15))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_76411,c_170]) ).

tcf(c_87030,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_16))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_76412,c_170]) ).

tcf(c_87031,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_17))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_76413,c_170]) ).

tcf(c_87032,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_18))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_76414,c_170]) ).

tcf(c_87033,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_76415,c_170]) ).

tcf(c_87034,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_13,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(iPr_def_13,X1))) ),
    inference(superposition,[status(thm)],[c_77366,c_170]) ).

tcf(c_87035,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK26(iPr_def_14)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78203,c_170]) ).

tcf(c_87036,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79573,c_170]) ).

tcf(c_87037,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_79414,c_170]) ).

tcf(c_87038,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_79557,c_170]) ).

tcf(c_87039,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_170]) ).

tcf(c_87040,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(m),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_79918,c_170]) ).

tcf(c_87041,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_79931,c_170]) ).

tcf(c_87042,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_83504,c_170]) ).

tcf(c_87043,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_170]) ).

tcf(c_87044,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(m),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_80664,c_170]) ).

tcf(c_87045,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_80677,c_170]) ).

tcf(c_87046,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_170]) ).

tcf(c_87047,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_170]) ).

tcf(c_87108,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(X0))) ),
    inference(light_normalisation,[status(thm)],[c_86982,c_59643]) ).

tcf(c_87374,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),
    inference(superposition,[status(thm)],[c_1563,c_86379]) ).

tcf(c_87375,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_46106]) ).

tcf(c_87376,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)))),X0) = pls,
    inference(superposition,[status(thm)],[c_87374,c_46104]) ).

tcf(c_87377,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_880]) ).

tcf(c_87378,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_608]) ).

tcf(c_87379,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_524]) ).

tcf(c_87380,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_523]) ).

tcf(c_87381,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_347]) ).

tcf(c_87382,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_346]) ).

tcf(c_87383,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15)),
    inference(superposition,[status(thm)],[c_87374,c_254]) ).

tcf(c_87386,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),
    inference(superposition,[status(thm)],[c_1563,c_86380]) ).

tcf(c_87387,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_46106]) ).

tcf(c_87388,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)))),X0) = pls,
    inference(superposition,[status(thm)],[c_87386,c_46104]) ).

tcf(c_87389,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_880]) ).

tcf(c_87390,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_608]) ).

tcf(c_87391,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_524]) ).

tcf(c_87392,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_523]) ).

tcf(c_87393,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_347]) ).

tcf(c_87394,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_346]) ).

tcf(c_87395,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16)),
    inference(superposition,[status(thm)],[c_87386,c_254]) ).

tcf(c_87452,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79573,c_86585]) ).

tcf(c_87453,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79414,c_86585]) ).

tcf(c_87454,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79557,c_86585]) ).

tcf(c_87455,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_86585]) ).

tcf(c_87456,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_79918,c_86585]) ).

tcf(c_87457,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_79931,c_86585]) ).

tcf(c_87458,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_83504,c_86585]) ).

tcf(c_87459,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_86585]) ).

tcf(c_87460,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0))) ),
    inference(superposition,[status(thm)],[c_80664,c_86585]) ).

tcf(c_87461,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_80677,c_86585]) ).

tcf(c_87462,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_86585]) ).

tcf(c_87463,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_86585]) ).

tcf(c_87464,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_86585,c_46112]) ).

tcf(c_87465,plain,
    ! [X0: $i] :
      ( ~ hBOOL(member_int(number_number_of_int(X0),d22set(sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_86585,c_1579]) ).

tcf(c_87466,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(number_number_of_int(X0),hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_86585,c_226]) ).

tcf(c_87516,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,sK30(iPr_def_19)),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_1720,c_86619]) ).

tcf(c_87539,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79573,c_86619]) ).

tcf(c_87540,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79414,c_86619]) ).

tcf(c_87541,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79557,c_86619]) ).

tcf(c_87542,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79437,c_86619]) ).

tcf(c_87543,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79918,c_86619]) ).

tcf(c_87544,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79931,c_86619]) ).

tcf(c_87545,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),m)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83504,c_86619]) ).

tcf(c_87546,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79957,c_86619]) ).

tcf(c_87547,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80664,c_86619]) ).

tcf(c_87548,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80677,c_86619]) ).

tcf(c_87549,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),m)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80692,c_86619]) ).

tcf(c_87550,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80705,c_86619]) ).

tcf(c_87551,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_86619,c_46112]) ).

tcf(c_87552,plain,
    ! [X0: $i] :
      ( ~ hBOOL(member_int(sK30(iPr_def_19),d22set(number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_86619,c_1579]) ).

tcf(c_87553,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(sK30(iPr_def_19),hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_86619,c_226]) ).

tcf(c_87630,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_1563,c_86999]) ).

tcf(c_87654,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79573,c_86999]) ).

tcf(c_87655,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79414,c_86999]) ).

tcf(c_87656,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79557,c_86999]) ).

tcf(c_87657,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_86999]) ).

tcf(c_87658,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79918,c_86999]) ).

tcf(c_87659,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79931,c_86999]) ).

tcf(c_87660,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83504,c_86999]) ).

tcf(c_87661,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_86999]) ).

tcf(c_87662,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80664,c_86999]) ).

tcf(c_87663,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80677,c_86999]) ).

tcf(c_87664,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_86999]) ).

tcf(c_87665,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_86999]) ).

tcf(c_87709,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0))))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_1563,c_87033]) ).

tcf(c_87711,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,sK30(iPr_def_19)),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_1720,c_87033]) ).

tcf(c_87734,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79573,c_87033]) ).

tcf(c_87735,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79414,c_87033]) ).

tcf(c_87736,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79557,c_87033]) ).

tcf(c_87737,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79437,c_87033]) ).

tcf(c_87738,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79918,c_87033]) ).

tcf(c_87739,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79931,c_87033]) ).

tcf(c_87740,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),m)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83504,c_87033]) ).

tcf(c_87741,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_79957,c_87033]) ).

tcf(c_87742,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80664,c_87033]) ).

tcf(c_87743,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80677,c_87033]) ).

tcf(c_87744,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),m)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80692,c_87033]) ).

tcf(c_87745,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_80705,c_87033]) ).

tcf(c_87817,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_80434,c_524]) ).

tcf(c_87820,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_80434,c_346]) ).

tcf(c_87821,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_80434,c_254]) ).

tcf(c_87822,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_15) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_83841,c_59639,c_76874]) ).

tcf(c_87828,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_84091,c_930]) ).

tcf(c_87832,plain,
    hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),zero_zero_real) = number267125858f_real(hAPP_int_int(plus_plus_int(pls),pls)),
    inference(superposition,[status(thm)],[c_568,c_408]) ).

tcf(c_87833,plain,
    hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),
    inference(superposition,[status(thm)],[c_78124,c_408]) ).

tcf(c_87834,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_408]) ).

tcf(c_87835,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(number_number_of_int(X0))) = number267125858f_real(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_388,c_408]) ).

tcf(c_87837,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_408,c_1043]) ).

tcf(c_87839,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X0)),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_408,c_1040]) ).

tcf(c_87840,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(X0)) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)),
    inference(superposition,[status(thm)],[c_408,c_373]) ).

tcf(c_87841,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),number267125858f_real(X1))) ),
    inference(superposition,[status(thm)],[c_408,c_138]) ).

tcf(c_87842,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_408,c_137]) ).

tcf(c_87843,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_408,c_45918]) ).

tcf(c_87844,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_408,c_631]) ).

tcf(c_87845,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),zero_zero_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_408,c_630]) ).

tcf(c_87846,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)))) ),
    inference(superposition,[status(thm)],[c_408,c_627]) ).

tcf(c_87847,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X0))) ),
    inference(superposition,[status(thm)],[c_408,c_626]) ).

tcf(c_87848,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_408,c_625]) ).

tcf(c_87849,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),zero_zero_real))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_408,c_624]) ).

tcf(c_87850,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),X0)),X1)),
    inference(superposition,[status(thm)],[c_408,c_878]) ).

tcf(c_87851,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),X1)),
    inference(superposition,[status(thm)],[c_408,c_389]) ).

tcf(c_87852,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0))),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),X1)),
    inference(superposition,[status(thm)],[c_408,c_383]) ).

tcf(c_87853,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X1)))) ),
    inference(superposition,[status(thm)],[c_408,c_138]) ).

tcf(c_87854,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X1),X1))) ),
    inference(superposition,[status(thm)],[c_408,c_137]) ).

tcf(c_87855,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(minus_minus_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X1))) = number267125858f_real(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),
    inference(superposition,[status(thm)],[c_408,c_878]) ).

tcf(c_87856,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X1))) = number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),
    inference(superposition,[status(thm)],[c_408,c_389]) ).

tcf(c_87857,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X1))) = number267125858f_real(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),
    inference(superposition,[status(thm)],[c_408,c_383]) ).

tcf(c_87858,plain,
    hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),one_one_real) = number267125858f_real(iPr_def_14),
    inference(light_normalisation,[status(thm)],[c_87833,c_59636,c_59638]) ).

tcf(c_87859,plain,
    hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),zero_zero_real) = zero_zero_real,
    inference(light_normalisation,[status(thm)],[c_87832,c_340,c_568]) ).

tcf(c_87860,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(number_number_of_int(X0))) = number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(light_normalisation,[status(thm)],[c_87835,c_79988]) ).

tcf(c_87981,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(X0),X0) != pls ) ),
    inference(superposition,[status(thm)],[c_82861,c_488]) ).

tcf(c_88011,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( hAPP_int_int(times_times_int(iPr_def_14),X0) != pls ) ),
    inference(superposition,[status(thm)],[c_79150,c_519]) ).

tcf(c_88014,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(X0) = pls )
      | ~ is_int(number_number_of_int(X0))
      | ( number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) != pls ) ),
    inference(superposition,[status(thm)],[c_388,c_519]) ).

tcf(c_88015,plain,
    ( ( pls = m )
    | ~ is_int(m)
    | ( hAPP_int_int(iPr_def_13,iPr_def_14) != pls ) ),
    inference(superposition,[status(thm)],[c_79190,c_519]) ).

tcf(c_88016,plain,
    ( ( one_one_int = pls )
    | ~ is_int(one_one_int)
    | ( hAPP_int_int(iPr_def_12,one_one_int) != pls ) ),
    inference(superposition,[status(thm)],[c_59636,c_519]) ).

tcf(c_88017,plain,
    ( ( one_one_int = pls )
    | ~ is_int(one_one_int)
    | ( pls != iPr_def_14 ) ),
    inference(light_normalisation,[status(thm)],[c_88016,c_59638]) ).

tcf(c_88018,plain,
    pls != iPr_def_14,
    inference(forward_subsumption_resolution,[status(thm)],[c_88017,c_1010,c_49]) ).

tcf(c_88019,plain,
    ( ( pls = m )
    | ( hAPP_int_int(iPr_def_13,iPr_def_14) != pls ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_88015,c_70]) ).

tcf(c_88025,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(X0) = pls )
      | ~ is_int(number_number_of_int(X0))
      | ( hAPP_int_int(times_times_int(iPr_def_14),X0) != pls ) ),
    inference(light_normalisation,[status(thm)],[c_88014,c_79988]) ).

tcf(c_88029,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79150,c_584]) ).

tcf(c_88032,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_82861,c_584]) ).

tcf(c_88034,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_382,c_584]) ).

tcf(c_88035,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_1001,c_584]) ).

tcf(c_88036,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79464,c_584]) ).

tcf(c_88038,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79150,c_584]) ).

tcf(c_88039,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_59637,c_584]) ).

tcf(c_88040,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_584]) ).

tcf(c_88042,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),number_number_of_int(hAPP_int_int(times_times_int(X1),X1))))),
    inference(superposition,[status(thm)],[c_382,c_584]) ).

tcf(c_88043,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls))),
    inference(superposition,[status(thm)],[c_1001,c_584]) ).

tcf(c_88044,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),one_one_int))),
    inference(superposition,[status(thm)],[c_79464,c_584]) ).

tcf(c_88046,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79150,c_584]) ).

tcf(c_88047,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(iPr_def_13,m)))),
    inference(superposition,[status(thm)],[c_59637,c_584]) ).

tcf(c_88048,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_584,c_226]) ).

tcf(c_88050,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_88036,c_59636]) ).

tcf(c_88064,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),
    inference(superposition,[status(thm)],[c_1563,c_86381]) ).

tcf(c_88065,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_46106]) ).

tcf(c_88066,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88064,c_46104]) ).

tcf(c_88067,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_880]) ).

tcf(c_88068,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_608]) ).

tcf(c_88069,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_524]) ).

tcf(c_88070,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_523]) ).

tcf(c_88071,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_347]) ).

tcf(c_88072,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_346]) ).

tcf(c_88073,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18))) = sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_18)),
    inference(superposition,[status(thm)],[c_88064,c_254]) ).

tcf(c_88101,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),
    inference(superposition,[status(thm)],[c_1563,c_86382]) ).

tcf(c_88112,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_80435,c_524]) ).

tcf(c_88115,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_80435,c_346]) ).

tcf(c_88116,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_80435,c_254]) ).

tcf(c_88120,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)))
      | ( X0 = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_491,c_80436]) ).

tcf(c_88124,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_82861,c_80436]) ).

tcf(c_88142,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80425,c_80436]) ).

tcf(c_88143,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_80528,c_80436]) ).

tcf(c_88149,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_80436,c_524]) ).

tcf(c_88152,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_80436,c_346]) ).

tcf(c_88153,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_80436,c_254]) ).

tcf(c_88154,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))))
      | ( X0 = zero_zero_nat ) ),
    inference(light_normalisation,[status(thm)],[c_88120,c_80269]) ).

tcf(c_88164,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)) != pls,
    inference(demodulation,[status(thm)],[c_84143,c_257]) ).

tcf(c_88165,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(iPr_def_13,m))) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_84298,c_256,c_257]) ).

tcf(c_88167,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),
    inference(demodulation,[status(thm)],[c_84303,c_257]) ).

tcf(c_88168,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_46106]) ).

tcf(c_88169,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88167,c_46104]) ).

tcf(c_88170,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_880]) ).

tcf(c_88171,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_608]) ).

tcf(c_88172,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_524]) ).

tcf(c_88173,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_523]) ).

tcf(c_88174,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_347]) ).

tcf(c_88175,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_346]) ).

tcf(c_88176,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(min),m))),
    inference(superposition,[status(thm)],[c_88167,c_254]) ).

tcf(c_88204,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),
    inference(demodulation,[status(thm)],[c_84304,c_76874]) ).

tcf(c_88205,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_46106]) ).

tcf(c_88206,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88204,c_46104]) ).

tcf(c_88207,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_880]) ).

tcf(c_88208,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_608]) ).

tcf(c_88209,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_524]) ).

tcf(c_88210,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_523]) ).

tcf(c_88211,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_347]) ).

tcf(c_88212,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_346]) ).

tcf(c_88213,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))),
    inference(superposition,[status(thm)],[c_88204,c_254]) ).

tcf(c_88218,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)))),
    inference(superposition,[status(thm)],[c_14792,c_585]) ).

tcf(c_88219,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X0)))),
    inference(superposition,[status(thm)],[c_373,c_585]) ).

tcf(c_88220,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),iPr_def_11)),hAPP_real_real(times_times_real(X1),X1)))),
    inference(superposition,[status(thm)],[c_82839,c_585]) ).

tcf(c_88221,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),hAPP_real_real(times_times_real(X0),X0)))),
    inference(superposition,[status(thm)],[c_325,c_585]) ).

tcf(c_88223,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(times_times_int(X0),X0))),hAPP_real_real(times_times_real(X1),X1)))),
    inference(superposition,[status(thm)],[c_383,c_585]) ).

tcf(c_88224,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))),
    inference(superposition,[status(thm)],[c_1002,c_585]) ).

tcf(c_88226,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_nat_real(power_power_real(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82839,c_585]) ).

tcf(c_88227,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),one_one_real))),
    inference(superposition,[status(thm)],[c_325,c_585]) ).

tcf(c_88229,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),number267125858f_real(hAPP_int_int(times_times_int(X1),X1))))),
    inference(superposition,[status(thm)],[c_383,c_585]) ).

tcf(c_88230,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),zero_zero_real))),
    inference(superposition,[status(thm)],[c_1002,c_585]) ).

tcf(c_88232,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(number267125858f_real(X0)),iPr_def_11)),hAPP_real_real(times_times_real(X1),X1)))),
    inference(light_normalisation,[status(thm)],[c_88223,c_82848]) ).

tcf(c_88247,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_786,c_594]) ).

tcf(c_88248,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78282,c_594]) ).

tcf(c_88249,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78547,c_594]) ).

tcf(c_88250,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_786,c_594]) ).

tcf(c_88251,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),min))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_78282,c_594]) ).

tcf(c_88252,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),iPr_def_14))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_78547,c_594]) ).

tcf(c_88269,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(zcong(X1,X0)))
      | is_int(sK14(X1,X0,X2))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_852]) ).

tcf(c_88270,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(X0,X0,X1))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_815,c_852]) ).

tcf(c_88271,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(X1,X0,one_one_int))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_829,c_852]) ).

tcf(c_88272,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(X2),X1),hAPP_int_int(times_times_int(X0),X1),X1))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_833,c_852]) ).

tcf(c_88273,plain,
    ! [X0: $i] :
      ( is_int(sK14(X0,pls,X0))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_913,c_852]) ).

tcf(c_88274,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(X0,hAPP_int_int(div_mod_int(X0),X1),X1))
      | ~ is_int(hAPP_int_int(div_mod_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_1699,c_852]) ).

tcf(c_88275,plain,
    ! [X0: $i] :
      ( is_int(sK14(X0,pls,min))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_76661,c_852]) ).

tcf(c_88276,plain,
    ! [X0: $i] :
      ( is_int(sK14(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_78307,c_852]) ).

tcf(c_88277,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_78328,c_852]) ).

tcf(c_88278,plain,
    ! [X0: $i] :
      ( is_int(sK14(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_78397,c_852]) ).

tcf(c_88279,plain,
    ( is_int(sK14(sK30(iPr_def_19),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19)))
    | ~ is_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_78401,c_852]) ).

tcf(c_88280,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_78405,c_852]) ).

tcf(c_88281,plain,
    ( is_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))
    | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_78409,c_852]) ).

tcf(c_88282,plain,
    ! [X0: $i] :
      ( is_int(sK14(pls,X0,X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_80619,c_852]) ).

tcf(c_88283,plain,
    ! [X0: $i] :
      ( is_int(sK14(pls,X0,min))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_80621,c_852]) ).

tcf(c_88284,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_81086,c_852]) ).

tcf(c_88285,plain,
    ( is_int(sK14(iPr_def_17,pls,iPr_def_16))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_81088,c_852]) ).

tcf(c_88286,plain,
    ( is_int(sK14(iPr_def_17,pls,m))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_81089,c_852]) ).

tcf(c_88287,plain,
    ( is_int(sK14(pls,iPr_def_17,iPr_def_16))
    | ~ is_int(iPr_def_17) ),
    inference(superposition,[status(thm)],[c_81152,c_852]) ).

tcf(c_88288,plain,
    ( is_int(sK14(pls,iPr_def_17,m))
    | ~ is_int(iPr_def_17) ),
    inference(superposition,[status(thm)],[c_81160,c_852]) ).

tcf(c_88289,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),pls,X0))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_83491,c_852]) ).

tcf(c_88290,plain,
    ( is_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),pls,m))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_84082,c_852]) ).

tcf(c_88291,plain,
    ( is_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),pls,sK30(iPr_def_19)))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_84091,c_852]) ).

tcf(c_88292,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),pls,X0))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_84092,c_852]) ).

tcf(c_88293,plain,
    ! [X0: $i] :
      ( is_int(sK14(pls,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),X0))
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_84098,c_852]) ).

tcf(c_88294,plain,
    is_int(sK14(pls,iPr_def_17,m)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88288,c_76349]) ).

tcf(c_88295,plain,
    is_int(sK14(pls,iPr_def_17,iPr_def_16)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88287,c_76349]) ).

tcf(c_88296,plain,
    is_int(sK14(iPr_def_17,pls,m)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88286,c_57]) ).

tcf(c_88297,plain,
    is_int(sK14(iPr_def_17,pls,iPr_def_16)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88285,c_57]) ).

tcf(c_88302,plain,
    ! [X0: $i] : is_int(sK14(X0,pls,min)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88275,c_57]) ).

tcf(c_88303,plain,
    ! [X0: $i] : is_int(sK14(X0,pls,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88273,c_57]) ).

tcf(c_88308,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88284,c_57]) ).

tcf(c_88309,plain,
    is_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),pls,m)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88290,c_57]) ).

tcf(c_88310,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),pls,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88292,c_57]) ).

tcf(c_88311,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),pls,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_88289,c_57]) ).

tcf(c_88312,plain,
    is_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),pls,sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_88291,c_57]) ).

tcf(c_88316,plain,
    is_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_88281,c_76385]) ).

tcf(c_88319,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_88280,c_76385]) ).

tcf(c_88320,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_88277,c_76385]) ).

tcf(c_88323,plain,
    is_int(sK14(sK30(iPr_def_19),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_88279,c_77054]) ).

tcf(c_88380,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(times_times_nat(iPr_def_11),X0) ) ),
    inference(superposition,[status(thm)],[c_79342,c_1287]) ).

tcf(c_88381,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(plus_plus_nat(X1),X2) ) ),
    inference(superposition,[status(thm)],[c_1284,c_1287]) ).

tcf(c_88382,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = one_one_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(iPr_def_10,X0) ) ),
    inference(superposition,[status(thm)],[c_77521,c_1287]) ).

tcf(c_88383,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) != X1 ) ),
    inference(superposition,[status(thm)],[c_1326,c_1287]) ).

tcf(c_88385,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(iPr_def_10,X0) != hAPP_nat_nat(iPr_def_10,X1) ) ),
    inference(superposition,[status(thm)],[c_59634,c_1287]) ).

tcf(c_88397,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_46106]) ).

tcf(c_88398,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,t)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88101,c_46104]) ).

tcf(c_88399,plain,
    hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_880]) ).

tcf(c_88400,plain,
    hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_608]) ).

tcf(c_88401,plain,
    hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_524]) ).

tcf(c_88402,plain,
    hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,t))) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_523]) ).

tcf(c_88403,plain,
    hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,t))) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_347]) ).

tcf(c_88404,plain,
    hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_346]) ).

tcf(c_88405,plain,
    number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,t))) = sK30(hAPP_i1948725293t_bool(ord_less_int,t)),
    inference(superposition,[status(thm)],[c_88101,c_254]) ).

tcf(c_88472,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,iPr_def_17,m)),X0)) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_46106]) ).

tcf(c_88473,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,iPr_def_17,m))),X0) = pls,
    inference(superposition,[status(thm)],[c_88294,c_46104]) ).

tcf(c_88474,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,iPr_def_17,m)),pls) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_880]) ).

tcf(c_88475,plain,
    hAPP_nat_int(power_power_int(sK14(pls,iPr_def_17,m)),one_one_nat) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_608]) ).

tcf(c_88476,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,iPr_def_17,m)),pls) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_524]) ).

tcf(c_88477,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,iPr_def_17,m)) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_523]) ).

tcf(c_88478,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,iPr_def_17,m)) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_347]) ).

tcf(c_88479,plain,
    hAPP_int_int(times_times_int(sK14(pls,iPr_def_17,m)),one_one_int) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_346]) ).

tcf(c_88480,plain,
    number_number_of_int(sK14(pls,iPr_def_17,m)) = sK14(pls,iPr_def_17,m),
    inference(superposition,[status(thm)],[c_88294,c_254]) ).

tcf(c_88483,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,iPr_def_17,iPr_def_16)),X0)) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_46106]) ).

tcf(c_88484,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,iPr_def_17,iPr_def_16))),X0) = pls,
    inference(superposition,[status(thm)],[c_88295,c_46104]) ).

tcf(c_88485,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,iPr_def_17,iPr_def_16)),pls) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_880]) ).

tcf(c_88486,plain,
    hAPP_nat_int(power_power_int(sK14(pls,iPr_def_17,iPr_def_16)),one_one_nat) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_608]) ).

tcf(c_88487,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,iPr_def_17,iPr_def_16)),pls) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_524]) ).

tcf(c_88488,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,iPr_def_17,iPr_def_16)) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_523]) ).

tcf(c_88489,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,iPr_def_17,iPr_def_16)) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_347]) ).

tcf(c_88490,plain,
    hAPP_int_int(times_times_int(sK14(pls,iPr_def_17,iPr_def_16)),one_one_int) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_346]) ).

tcf(c_88491,plain,
    number_number_of_int(sK14(pls,iPr_def_17,iPr_def_16)) = sK14(pls,iPr_def_17,iPr_def_16),
    inference(superposition,[status(thm)],[c_88295,c_254]) ).

tcf(c_88494,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_46106]) ).

tcf(c_88495,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88316,c_46104]) ).

tcf(c_88496,plain,
    hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_880]) ).

tcf(c_88497,plain,
    hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_608]) ).

tcf(c_88498,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_524]) ).

tcf(c_88499,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_523]) ).

tcf(c_88500,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_347]) ).

tcf(c_88501,plain,
    hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_346]) ).

tcf(c_88502,plain,
    number_number_of_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88316,c_254]) ).

tcf(c_88505,plain,
    is_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_88319]) ).

tcf(c_88508,plain,
    is_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_1001,c_88319]) ).

tcf(c_88513,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_46106]) ).

tcf(c_88514,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88319,c_46104]) ).

tcf(c_88515,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_880]) ).

tcf(c_88516,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_608]) ).

tcf(c_88517,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_524]) ).

tcf(c_88518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_523]) ).

tcf(c_88519,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_347]) ).

tcf(c_88520,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_346]) ).

tcf(c_88521,plain,
    ! [X0: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88319,c_254]) ).

tcf(c_88548,plain,
    is_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76995,c_88320]) ).

tcf(c_88550,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_46106]) ).

tcf(c_88551,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88320,c_46104]) ).

tcf(c_88552,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_880]) ).

tcf(c_88553,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_608]) ).

tcf(c_88554,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_524]) ).

tcf(c_88555,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_523]) ).

tcf(c_88556,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_347]) ).

tcf(c_88557,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_346]) ).

tcf(c_88558,plain,
    ! [X0: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88320,c_254]) ).

tcf(c_88612,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_46106]) ).

tcf(c_88613,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88508,c_46104]) ).

tcf(c_88614,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_880]) ).

tcf(c_88615,plain,
    hAPP_nat_int(power_power_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_608]) ).

tcf(c_88616,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_524]) ).

tcf(c_88617,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_523]) ).

tcf(c_88618,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_347]) ).

tcf(c_88619,plain,
    hAPP_int_int(times_times_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_346]) ).

tcf(c_88620,plain,
    number_number_of_int(sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88508,c_254]) ).

tcf(c_88623,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_46106]) ).

tcf(c_88624,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88548,c_46104]) ).

tcf(c_88625,plain,
    hAPP_int_int(minus_minus_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_880]) ).

tcf(c_88626,plain,
    hAPP_nat_int(power_power_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_608]) ).

tcf(c_88627,plain,
    hAPP_int_int(plus_plus_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_524]) ).

tcf(c_88628,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_523]) ).

tcf(c_88629,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_347]) ).

tcf(c_88630,plain,
    hAPP_int_int(times_times_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_346]) ).

tcf(c_88631,plain,
    number_number_of_int(sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(sK30(iPr_def_19),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88548,c_254]) ).

tcf(c_88634,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_46106]) ).

tcf(c_88635,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_88505,c_46104]) ).

tcf(c_88636,plain,
    hAPP_int_int(minus_minus_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_880]) ).

tcf(c_88637,plain,
    hAPP_nat_int(power_power_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_608]) ).

tcf(c_88638,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_524]) ).

tcf(c_88639,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_523]) ).

tcf(c_88640,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_347]) ).

tcf(c_88641,plain,
    hAPP_int_int(times_times_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_346]) ).

tcf(c_88642,plain,
    number_number_of_int(sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88505,c_254]) ).

tcf(c_88646,plain,
    hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_88495]) ).

tcf(c_88647,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),X0) = pls,
    inference(superposition,[status(thm)],[c_253,c_88495]) ).

tcf(c_88650,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_88495]) ).

tcf(c_88651,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_88495,c_76662]) ).

tcf(c_88653,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls),X0)),
    inference(superposition,[status(thm)],[c_88495,c_1698]) ).

tcf(c_88692,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_88514]) ).

tcf(c_88693,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),X1) = pls,
    inference(superposition,[status(thm)],[c_253,c_88514]) ).

tcf(c_88696,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_88514]) ).

tcf(c_88705,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_88514,c_76662]) ).

tcf(c_88707,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),pls),X0)),
    inference(superposition,[status(thm)],[c_88514,c_1698]) ).

tcf(c_88750,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(times_times_nat(iPr_def_11),X1) ) ),
    inference(superposition,[status(thm)],[c_79342,c_1288]) ).

tcf(c_88752,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),one_one_nat) != hAPP_nat_nat(iPr_def_10,X1) ) ),
    inference(superposition,[status(thm)],[c_77521,c_1288]) ).

tcf(c_88754,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) != X1 ) ),
    inference(superposition,[status(thm)],[c_1325,c_1288]) ).

tcf(c_88755,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = one_one_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) != hAPP_nat_nat(iPr_def_10,X1) ) ),
    inference(superposition,[status(thm)],[c_59634,c_1288]) ).

tcf(c_88769,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | ( hAPP_nat_nat(minus_minus_nat(X0),sK35(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,X0))) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1332]) ).

tcf(c_88770,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
      | ( hAPP_nat_nat(div_mod_nat(X0),sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0))) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1693]) ).

tcf(c_88771,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1364]) ).

tcf(c_88772,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),zero_zero_nat))
      | ( sK35(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1577,c_1590]) ).

tcf(c_88777,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_88771,c_1317]) ).

tcf(c_88780,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0))) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_88770,c_1317]) ).

tcf(c_88792,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(zero_zero_nat),sK36(X0,X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1582,c_1693]) ).

tcf(c_88793,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),sK36(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1582,c_1364]) ).

tcf(c_88797,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)))),
    inference(light_normalisation,[status(thm)],[c_14940,c_59634,c_59635]) ).

tcf(c_88798,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ( hAPP_nat_nat(times_times_nat(iPr_def_11),X0) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_491,c_88797]) ).

tcf(c_88801,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_1309,c_88797]) ).

tcf(c_88804,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),zero_zero_nat))),
    inference(superposition,[status(thm)],[c_1337,c_88797]) ).

tcf(c_88805,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_88797,c_226]) ).

tcf(c_88809,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(iPr_def_17,pls,m)),X0)) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_46106]) ).

tcf(c_88810,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(iPr_def_17,pls,m))),X0) = pls,
    inference(superposition,[status(thm)],[c_88296,c_46104]) ).

tcf(c_88811,plain,
    hAPP_int_int(minus_minus_int(sK14(iPr_def_17,pls,m)),pls) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_880]) ).

tcf(c_88812,plain,
    hAPP_nat_int(power_power_int(sK14(iPr_def_17,pls,m)),one_one_nat) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_608]) ).

tcf(c_88813,plain,
    hAPP_int_int(plus_plus_int(sK14(iPr_def_17,pls,m)),pls) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_524]) ).

tcf(c_88814,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(iPr_def_17,pls,m)) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_523]) ).

tcf(c_88815,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(iPr_def_17,pls,m)) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_347]) ).

tcf(c_88816,plain,
    hAPP_int_int(times_times_int(sK14(iPr_def_17,pls,m)),one_one_int) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_346]) ).

tcf(c_88817,plain,
    number_number_of_int(sK14(iPr_def_17,pls,m)) = sK14(iPr_def_17,pls,m),
    inference(superposition,[status(thm)],[c_88296,c_254]) ).

tcf(c_88852,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(iPr_def_17,pls,iPr_def_16)),X0)) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_46106]) ).

tcf(c_88853,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(iPr_def_17,pls,iPr_def_16))),X0) = pls,
    inference(superposition,[status(thm)],[c_88297,c_46104]) ).

tcf(c_88854,plain,
    hAPP_int_int(minus_minus_int(sK14(iPr_def_17,pls,iPr_def_16)),pls) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_880]) ).

tcf(c_88855,plain,
    hAPP_nat_int(power_power_int(sK14(iPr_def_17,pls,iPr_def_16)),one_one_nat) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_608]) ).

tcf(c_88856,plain,
    hAPP_int_int(plus_plus_int(sK14(iPr_def_17,pls,iPr_def_16)),pls) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_524]) ).

tcf(c_88857,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(iPr_def_17,pls,iPr_def_16)) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_523]) ).

tcf(c_88858,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(iPr_def_17,pls,iPr_def_16)) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_347]) ).

tcf(c_88859,plain,
    hAPP_int_int(times_times_int(sK14(iPr_def_17,pls,iPr_def_16)),one_one_int) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_346]) ).

tcf(c_88860,plain,
    number_number_of_int(sK14(iPr_def_17,pls,iPr_def_16)) = sK14(iPr_def_17,pls,iPr_def_16),
    inference(superposition,[status(thm)],[c_88297,c_254]) ).

tcf(c_88863,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(X1,pls,min)),X0)) = sK14(X1,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_46106]) ).

tcf(c_88864,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(X1,pls,min))),X0) = pls,
    inference(superposition,[status(thm)],[c_88302,c_46104]) ).

tcf(c_88865,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(X0,pls,min)),pls) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_880]) ).

tcf(c_88866,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(X0,pls,min)),one_one_nat) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_608]) ).

tcf(c_88867,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(X0,pls,min)),pls) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_524]) ).

tcf(c_88868,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(X0,pls,min)) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_523]) ).

tcf(c_88869,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(X0,pls,min)) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_347]) ).

tcf(c_88870,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(X0,pls,min)),one_one_int) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_346]) ).

tcf(c_88871,plain,
    ! [X0: $i] : number_number_of_int(sK14(X0,pls,min)) = sK14(X0,pls,min),
    inference(superposition,[status(thm)],[c_88302,c_254]) ).

tcf(c_88881,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(X1,pls,X1)),X0)) = sK14(X1,pls,X1),
    inference(superposition,[status(thm)],[c_88303,c_46106]) ).

tcf(c_88882,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(X1,pls,X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_88303,c_46104]) ).

tcf(c_88883,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(X0,pls,X0)),pls) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_880]) ).

tcf(c_88884,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(X0,pls,X0)),one_one_nat) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_608]) ).

tcf(c_88885,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(X0,pls,X0)),pls) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_524]) ).

tcf(c_88886,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(X0,pls,X0)) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_523]) ).

tcf(c_88887,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(X0,pls,X0)) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_347]) ).

tcf(c_88888,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(X0,pls,X0)),one_one_int) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_346]) ).

tcf(c_88889,plain,
    ! [X0: $i] : number_number_of_int(sK14(X0,pls,X0)) = sK14(X0,pls,X0),
    inference(superposition,[status(thm)],[c_88303,c_254]) ).

tcf(c_88899,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_88551]) ).

tcf(c_88900,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),X1) = pls,
    inference(superposition,[status(thm)],[c_253,c_88551]) ).

tcf(c_88903,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_88551]) ).

tcf(c_88910,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_88551,c_76662]) ).

tcf(c_88912,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls),X0)),
    inference(superposition,[status(thm)],[c_88551,c_1698]) ).

tcf(c_88928,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_88502,c_170]) ).

tcf(c_88929,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) ),
    inference(superposition,[status(thm)],[c_88502,c_169]) ).

tcf(c_88930,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88502,c_45982]) ).

tcf(c_88931,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88502,c_45978]) ).

tcf(c_88932,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88502,c_45914]) ).

tcf(c_88933,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80531]) ).

tcf(c_88934,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_88502,c_85003]) ).

tcf(c_88935,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88502,c_84396]) ).

tcf(c_88936,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88502,c_83525]) ).

tcf(c_88939,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80530]) ).

tcf(c_88940,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80528]) ).

tcf(c_88941,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80527]) ).

tcf(c_88942,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88502,c_80428]) ).

tcf(c_88943,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88502,c_80427]) ).

tcf(c_88944,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88502,c_80425]) ).

tcf(c_88945,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88502,c_80424]) ).

tcf(c_88947,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_81465]) ).

tcf(c_88948,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88502,c_81315]) ).

tcf(c_88949,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_88502,c_879]) ).

tcf(c_88950,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_80314]) ).

tcf(c_88951,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80313]) ).

tcf(c_88952,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_80257]) ).

tcf(c_88953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_88502,c_388]) ).

tcf(c_88954,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_88502,c_79563]) ).

tcf(c_88957,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_88502,c_382]) ).

tcf(c_88959,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88502,c_170]) ).

tcf(c_88960,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88502,c_169]) ).

tcf(c_88961,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88502,c_83642]) ).

tcf(c_88962,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_83641]) ).

tcf(c_88963,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88502,c_83009]) ).

tcf(c_88964,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88502,c_83008]) ).

tcf(c_88965,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_879]) ).

tcf(c_88966,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_388]) ).

tcf(c_88967,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_79563]) ).

tcf(c_88968,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_382]) ).

tcf(c_89083,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88950,c_524]) ).

tcf(c_89086,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88950,c_346]) ).

tcf(c_89087,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88950,c_254]) ).

tcf(c_89096,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)))),
    inference(light_normalisation,[status(thm)],[c_14941,c_59634,c_59635]) ).

tcf(c_89097,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),zero_zero_real))
      | ( hAPP_nat_nat(times_times_nat(iPr_def_11),X0) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_495,c_89096]) ).

tcf(c_89100,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_1309,c_89096]) ).

tcf(c_89103,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),zero_zero_nat))),
    inference(superposition,[status(thm)],[c_1337,c_89096]) ).

tcf(c_89110,plain,
    ! [X0: $i] :
      ( is_int(sK30(cOMBC_int_int_bool(ord_less_int,one_one_int)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real)) ),
    inference(superposition,[status(thm)],[c_1563,c_45890]) ).

tcf(c_89111,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(pls)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_45890]) ).

tcf(c_89112,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(min)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),min)) ),
    inference(superposition,[status(thm)],[c_76397,c_45890]) ).

tcf(c_89113,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(one_one_int)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76393,c_45890]) ).

tcf(c_89114,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(undefined_int(int))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_76395,c_45890]) ).

tcf(c_89115,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(twoSqu1241645765sum2sq(X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),twoSqu1241645765sum2sq(X0))) ),
    inference(superposition,[status(thm)],[c_76399,c_45890]) ).

tcf(c_89116,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_nat_int(X0,X1))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_nat_int(X0,X1))) ),
    inference(superposition,[status(thm)],[c_76401,c_45890]) ).

tcf(c_89117,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(m)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_76402,c_45890]) ).

tcf(c_89118,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(s1)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),s1)) ),
    inference(superposition,[status(thm)],[c_76403,c_45890]) ).

tcf(c_89119,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(s)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),s)) ),
    inference(superposition,[status(thm)],[c_76404,c_45890]) ).

tcf(c_89120,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(t)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),t)) ),
    inference(superposition,[status(thm)],[c_76405,c_45890]) ).

tcf(c_89121,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK9)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK9)) ),
    inference(superposition,[status(thm)],[c_76406,c_45890]) ).

tcf(c_89122,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK10)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK10)) ),
    inference(superposition,[status(thm)],[c_76407,c_45890]) ).

tcf(c_89123,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK11)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK11)) ),
    inference(superposition,[status(thm)],[c_76408,c_45890]) ).

tcf(c_89124,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK13)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK13)) ),
    inference(superposition,[status(thm)],[c_76409,c_45890]) ).

tcf(c_89125,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(iPr_def_14)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_76410,c_45890]) ).

tcf(c_89126,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(iPr_def_15)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_76411,c_45890]) ).

tcf(c_89127,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(iPr_def_16)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_76412,c_45890]) ).

tcf(c_89128,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(iPr_def_17)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_76413,c_45890]) ).

tcf(c_89129,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(iPr_def_18)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_76414,c_45890]) ).

tcf(c_89130,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK30(iPr_def_19))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_76415,c_45890]) ).

tcf(c_89131,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(iPr_def_13,X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(iPr_def_13,X0))) ),
    inference(superposition,[status(thm)],[c_77366,c_45890]) ).

tcf(c_89132,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK26(iPr_def_14))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78203,c_45890]) ).

tcf(c_89133,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79573,c_45890]) ).

tcf(c_89134,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79414,c_45890]) ).

tcf(c_89135,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79557,c_45890]) ).

tcf(c_89136,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_45890]) ).

tcf(c_89137,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(m),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79918,c_45890]) ).

tcf(c_89138,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79931,c_45890]) ).

tcf(c_89139,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),m))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83504,c_45890]) ).

tcf(c_89140,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_45890]) ).

tcf(c_89141,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(m),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80664,c_45890]) ).

tcf(c_89142,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80677,c_45890]) ).

tcf(c_89143,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),m))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_45890]) ).

tcf(c_89144,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_45890]) ).

tcf(c_89145,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88502,c_45890]) ).

tcf(c_89174,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_89113,c_78124]) ).

tcf(c_89175,plain,
    ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),one_one_int)),
    inference(forward_subsumption_resolution,[status(thm)],[c_89174,c_971]) ).

tcf(c_89178,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),pls)) ),
    inference(light_normalisation,[status(thm)],[c_89111,c_568]) ).

tcf(c_89246,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X0))) ),
    inference(light_normalisation,[status(thm)],[c_45894,c_59643]) ).

tcf(c_89254,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)))) ),
    inference(superposition,[status(thm)],[c_408,c_89246]) ).

tcf(c_89255,plain,
    ( hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(one_one_int)))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),one_one_real)) ),
    inference(superposition,[status(thm)],[c_78124,c_89246]) ).

tcf(c_89256,plain,
    ( hBOOL(hAPP_int_bool(iPr_def_19,one_one_int))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),one_one_real)) ),
    inference(light_normalisation,[status(thm)],[c_89255,c_76393]) ).

tcf(c_89257,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)))) ),
    inference(light_normalisation,[status(thm)],[c_89254,c_79988,c_87834]) ).

tcf(c_89265,plain,
    ! [X0: $i] :
      ( is_int(sK30(cOMBC_int_int_bool(ord_less_eq_int,one_one_int)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real)) ),
    inference(superposition,[status(thm)],[c_1563,c_45898]) ).

tcf(c_89266,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(pls)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_574,c_45898]) ).

tcf(c_89267,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(min)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),min)) ),
    inference(superposition,[status(thm)],[c_76397,c_45898]) ).

tcf(c_89268,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(one_one_int)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76393,c_45898]) ).

tcf(c_89269,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(undefined_int(int))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_76395,c_45898]) ).

tcf(c_89270,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(twoSqu1241645765sum2sq(X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),twoSqu1241645765sum2sq(X0))) ),
    inference(superposition,[status(thm)],[c_76399,c_45898]) ).

tcf(c_89271,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_nat_int(X0,X1))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(X0,X1))) ),
    inference(superposition,[status(thm)],[c_76401,c_45898]) ).

tcf(c_89272,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(m)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_76402,c_45898]) ).

tcf(c_89273,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(s1)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),s1)) ),
    inference(superposition,[status(thm)],[c_76403,c_45898]) ).

tcf(c_89274,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(s)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),s)) ),
    inference(superposition,[status(thm)],[c_76404,c_45898]) ).

tcf(c_89275,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(t)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),t)) ),
    inference(superposition,[status(thm)],[c_76405,c_45898]) ).

tcf(c_89276,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK9)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK9)) ),
    inference(superposition,[status(thm)],[c_76406,c_45898]) ).

tcf(c_89277,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK10)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK10)) ),
    inference(superposition,[status(thm)],[c_76407,c_45898]) ).

tcf(c_89278,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK11)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK11)) ),
    inference(superposition,[status(thm)],[c_76408,c_45898]) ).

tcf(c_89279,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK13)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK13)) ),
    inference(superposition,[status(thm)],[c_76409,c_45898]) ).

tcf(c_89280,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(iPr_def_14)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_76410,c_45898]) ).

tcf(c_89281,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(iPr_def_15)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_76411,c_45898]) ).

tcf(c_89282,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(iPr_def_16)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_76412,c_45898]) ).

tcf(c_89283,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(iPr_def_17)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_76413,c_45898]) ).

tcf(c_89284,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(iPr_def_18)),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_76414,c_45898]) ).

tcf(c_89285,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK30(iPr_def_19))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_76415,c_45898]) ).

tcf(c_89286,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(iPr_def_13,X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_13,X0))) ),
    inference(superposition,[status(thm)],[c_77366,c_45898]) ).

tcf(c_89287,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK26(iPr_def_14))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78203,c_45898]) ).

tcf(c_89288,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79573,c_45898]) ).

tcf(c_89289,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79414,c_45898]) ).

tcf(c_89290,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79557,c_45898]) ).

tcf(c_89291,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79437,c_45898]) ).

tcf(c_89292,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(plus_plus_int(m),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79918,c_45898]) ).

tcf(c_89293,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_79931,c_45898]) ).

tcf(c_89294,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),m))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83504,c_45898]) ).

tcf(c_89295,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_79957,c_45898]) ).

tcf(c_89296,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(m),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80664,c_45898]) ).

tcf(c_89297,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_80677,c_45898]) ).

tcf(c_89298,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),m))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))) ),
    inference(superposition,[status(thm)],[c_80692,c_45898]) ).

tcf(c_89299,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_80705,c_45898]) ).

tcf(c_89300,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88502,c_45898]) ).

tcf(c_89329,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_89268,c_78124]) ).

tcf(c_89332,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),pls)) ),
    inference(light_normalisation,[status(thm)],[c_89266,c_568]) ).

tcf(c_89435,plain,
    ! [X0: $i] : is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),
    inference(superposition,[status(thm)],[c_1563,c_86422]) ).

tcf(c_89457,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X1))),X0)) = sK30(hAPP_i1948725293t_bool(ord_less_int,X1)),
    inference(superposition,[status(thm)],[c_89435,c_46106]) ).

tcf(c_89458,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(hAPP_i1948725293t_bool(ord_less_int,X1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_89435,c_46104]) ).

tcf(c_89459,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_880]) ).

tcf(c_89460,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),one_one_nat) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_608]) ).

tcf(c_89461,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),pls) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_524]) ).

tcf(c_89462,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_523]) ).

tcf(c_89463,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_347]) ).

tcf(c_89464,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))),one_one_int) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_346]) ).

tcf(c_89465,plain,
    ! [X0: $i] : number_number_of_int(sK30(hAPP_i1948725293t_bool(ord_less_int,X0))) = sK30(hAPP_i1948725293t_bool(ord_less_int,X0)),
    inference(superposition,[status(thm)],[c_89435,c_254]) ).

tcf(c_89492,plain,
    is_int(sK14(pls,pls,pls)),
    inference(superposition,[status(thm)],[c_76363,c_88308]) ).

tcf(c_89493,plain,
    is_int(sK14(m,pls,one_one_int)),
    inference(superposition,[status(thm)],[c_76934,c_88308]) ).

tcf(c_89494,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),pls,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_88308]) ).

tcf(c_89495,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),pls,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_88308]) ).

tcf(c_89496,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,X1),pls,X1)),X0)) = sK14(hAPP_int_int(iPr_def_13,X1),pls,X1),
    inference(superposition,[status(thm)],[c_88308,c_46106]) ).

tcf(c_89497,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,X1),pls,X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_88308,c_46104]) ).

tcf(c_89498,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)),pls) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_880]) ).

tcf(c_89499,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_608]) ).

tcf(c_89500,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)),pls) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_524]) ).

tcf(c_89501,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_523]) ).

tcf(c_89502,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_347]) ).

tcf(c_89503,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)),one_one_int) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_346]) ).

tcf(c_89504,plain,
    ! [X0: $i] : number_number_of_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,X0)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,X0),
    inference(superposition,[status(thm)],[c_88308,c_254]) ).

tcf(c_89505,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),pls,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_89494,c_79321]) ).

tcf(c_89530,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(m,pls,one_one_int)),X0)) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_46106]) ).

tcf(c_89531,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(m,pls,one_one_int))),X0) = pls,
    inference(superposition,[status(thm)],[c_89493,c_46104]) ).

tcf(c_89532,plain,
    hAPP_int_int(minus_minus_int(sK14(m,pls,one_one_int)),pls) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_880]) ).

tcf(c_89533,plain,
    hAPP_nat_int(power_power_int(sK14(m,pls,one_one_int)),one_one_nat) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_608]) ).

tcf(c_89534,plain,
    hAPP_int_int(plus_plus_int(sK14(m,pls,one_one_int)),pls) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_524]) ).

tcf(c_89535,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(m,pls,one_one_int)) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_523]) ).

tcf(c_89536,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(m,pls,one_one_int)) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_347]) ).

tcf(c_89537,plain,
    hAPP_int_int(times_times_int(sK14(m,pls,one_one_int)),one_one_int) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_346]) ).

tcf(c_89538,plain,
    number_number_of_int(sK14(m,pls,one_one_int)) = sK14(m,pls,one_one_int),
    inference(superposition,[status(thm)],[c_89493,c_254]) ).

tcf(c_89550,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK30(iPr_def_19))),one_one_real))
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_89130,c_970]) ).

tcf(c_89558,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88500,c_1042]) ).

tcf(c_89559,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88500,c_833]) ).

tcf(c_89561,plain,
    hBOOL(member_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_88500,c_76535]) ).

tcf(c_89562,plain,
    hBOOL(member_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88500,c_76498]) ).

tcf(c_89563,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88500,c_1045]) ).

tcf(c_89564,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88500,c_833]) ).

tcf(c_89565,plain,
    hAPP_int_int(div_mod_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_88500,c_88495]) ).

tcf(c_89576,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88521,c_45898]) ).

tcf(c_89577,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88521,c_45890]) ).

tcf(c_89582,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_88521,c_170]) ).

tcf(c_89583,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_88521,c_169]) ).

tcf(c_89584,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88521,c_45982]) ).

tcf(c_89585,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88521,c_45978]) ).

tcf(c_89586,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88521,c_45914]) ).

tcf(c_89587,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80531]) ).

tcf(c_89588,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_88521,c_85003]) ).

tcf(c_89589,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88521,c_84396]) ).

tcf(c_89590,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88521,c_83525]) ).

tcf(c_89593,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80530]) ).

tcf(c_89594,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80528]) ).

tcf(c_89595,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80527]) ).

tcf(c_89596,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88521,c_80428]) ).

tcf(c_89597,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88521,c_80427]) ).

tcf(c_89598,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88521,c_80425]) ).

tcf(c_89599,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88521,c_80424]) ).

tcf(c_89601,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_81465]) ).

tcf(c_89602,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88521,c_81315]) ).

tcf(c_89603,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88521,c_879]) ).

tcf(c_89604,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_80314]) ).

tcf(c_89605,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80313]) ).

tcf(c_89606,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_80257]) ).

tcf(c_89607,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88521,c_388]) ).

tcf(c_89608,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_88521,c_79563]) ).

tcf(c_89611,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88521,c_382]) ).

tcf(c_89613,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88521,c_170]) ).

tcf(c_89614,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88521,c_169]) ).

tcf(c_89615,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88521,c_83642]) ).

tcf(c_89616,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_83641]) ).

tcf(c_89617,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88521,c_83009]) ).

tcf(c_89618,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88521,c_83008]) ).

tcf(c_89619,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_879]) ).

tcf(c_89620,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_388]) ).

tcf(c_89621,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_79563]) ).

tcf(c_89622,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_382]) ).

tcf(c_89738,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_82861,c_89604]) ).

tcf(c_89739,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_253,c_89604]) ).

tcf(c_89741,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(pls,sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_1001,c_89604]) ).

tcf(c_89750,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_89604,c_524]) ).

tcf(c_89753,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_89604,c_346]) ).

tcf(c_89754,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_89604,c_254]) ).

tcf(c_89781,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88558,c_45898]) ).

tcf(c_89782,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88558,c_45890]) ).

tcf(c_89787,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_88558,c_170]) ).

tcf(c_89788,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_88558,c_169]) ).

tcf(c_89789,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88558,c_45982]) ).

tcf(c_89790,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),pls)) ),
    inference(superposition,[status(thm)],[c_88558,c_45978]) ).

tcf(c_89791,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88558,c_45914]) ).

tcf(c_89792,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80531]) ).

tcf(c_89793,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)))),
    inference(superposition,[status(thm)],[c_88558,c_85003]) ).

tcf(c_89794,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88558,c_84396]) ).

tcf(c_89795,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88558,c_83525]) ).

tcf(c_89798,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80530]) ).

tcf(c_89799,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80528]) ).

tcf(c_89800,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80527]) ).

tcf(c_89801,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88558,c_80428]) ).

tcf(c_89802,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88558,c_80427]) ).

tcf(c_89803,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88558,c_80425]) ).

tcf(c_89804,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88558,c_80424]) ).

tcf(c_89806,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_81465]) ).

tcf(c_89807,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88558,c_81315]) ).

tcf(c_89808,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88558,c_879]) ).

tcf(c_89810,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80313]) ).

tcf(c_89811,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_80257]) ).

tcf(c_89812,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88558,c_388]) ).

tcf(c_89813,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_88558,c_79563]) ).

tcf(c_89816,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)),
    inference(superposition,[status(thm)],[c_88558,c_382]) ).

tcf(c_89818,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88558,c_170]) ).

tcf(c_89819,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88558,c_169]) ).

tcf(c_89820,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88558,c_83642]) ).

tcf(c_89821,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_83641]) ).

tcf(c_89822,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88558,c_83009]) ).

tcf(c_89823,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88558,c_83008]) ).

tcf(c_89824,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_879]) ).

tcf(c_89825,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_388]) ).

tcf(c_89826,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_79563]) ).

tcf(c_89827,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_382]) ).

tcf(c_89929,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),one_one_real))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_1241,c_45902]) ).

tcf(c_89931,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(pls)))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_568,c_45902]) ).

tcf(c_89932,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)))) ),
    inference(superposition,[status(thm)],[c_408,c_45902]) ).

tcf(c_89933,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(one_one_int)))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real)) ),
    inference(superposition,[status(thm)],[c_78124,c_45902]) ).

tcf(c_89934,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real)) ),
    inference(light_normalisation,[status(thm)],[c_89933,c_76393]) ).

tcf(c_89935,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)) ),
    inference(light_normalisation,[status(thm)],[c_89931,c_574]) ).

tcf(c_89936,plain,
    ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
    inference(forward_subsumption_resolution,[status(thm)],[c_89935,c_85740]) ).

tcf(c_89939,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)))) ),
    inference(light_normalisation,[status(thm)],[c_89932,c_79988,c_87834]) ).

tcf(c_89948,plain,
    hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(pls)) = one_one_real,
    inference(superposition,[status(thm)],[c_114,c_46164]) ).

tcf(c_89949,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real ) ),
    inference(superposition,[status(thm)],[c_1563,c_46164]) ).

tcf(c_89951,plain,
    hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(min)) = one_one_real,
    inference(superposition,[status(thm)],[c_774,c_46164]) ).

tcf(c_89952,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X0)) = one_one_real )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_46164]) ).

tcf(c_89953,plain,
    hAPP_nat_real(power_power_real(zero_zero_real),zero_zero_nat) = one_one_real,
    inference(light_normalisation,[status(thm)],[c_89951,c_78282]) ).

tcf(c_89964,plain,
    hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(pls)) = one_one_nat,
    inference(superposition,[status(thm)],[c_114,c_46166]) ).

tcf(c_89965,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat ) ),
    inference(superposition,[status(thm)],[c_1563,c_46166]) ).

tcf(c_89967,plain,
    hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(min)) = one_one_nat,
    inference(superposition,[status(thm)],[c_774,c_46166]) ).

tcf(c_89968,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X0)) = one_one_nat )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_46166]) ).

tcf(c_89969,plain,
    hAPP_nat_nat(power_power_nat(zero_zero_nat),zero_zero_nat) = one_one_nat,
    inference(light_normalisation,[status(thm)],[c_89967,c_78282]) ).

tcf(c_89996,plain,
    hAPP_nat_int(power_power_int(pls),number_number_of_nat(pls)) = one_one_int,
    inference(superposition,[status(thm)],[c_114,c_46168]) ).

tcf(c_89997,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_1563,c_46168]) ).

tcf(c_89999,plain,
    hAPP_nat_int(power_power_int(pls),number_number_of_nat(min)) = one_one_int,
    inference(superposition,[status(thm)],[c_774,c_46168]) ).

tcf(c_90000,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(X0)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_46168]) ).

tcf(c_90001,plain,
    hAPP_nat_int(power_power_int(pls),zero_zero_nat) = one_one_int,
    inference(light_normalisation,[status(thm)],[c_89999,c_78282]) ).

tcf(c_90012,plain,
    hBOOL(hAPP_int_bool(zcong(pls,pls),m)),
    inference(superposition,[status(thm)],[c_76363,c_81087]) ).

tcf(c_90013,plain,
    hBOOL(hAPP_int_bool(zcong(m,pls),m)),
    inference(superposition,[status(thm)],[c_76934,c_81087]) ).

tcf(c_90016,plain,
    ! [X0: $i] : hBOOL(member_int(m,zcong(hAPP_int_int(iPr_def_13,X0),pls))),
    inference(superposition,[status(thm)],[c_81087,c_226]) ).

tcf(c_90017,plain,
    ! [X0: $i] :
      ( is_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_81087,c_852]) ).

tcf(c_90018,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,X0)),m)),
    inference(superposition,[status(thm)],[c_81087,c_814]) ).

tcf(c_90019,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,X0)),m) = pls,
    inference(superposition,[status(thm)],[c_81087,c_1697]) ).

tcf(c_90020,plain,
    ! [X0: $i] : legendre(hAPP_int_int(iPr_def_13,X0),m) = pls,
    inference(superposition,[status(thm)],[c_81087,c_940]) ).

tcf(c_90022,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)),
    inference(forward_subsumption_resolution,[status(thm)],[c_90017,c_57]) ).

tcf(c_90029,plain,
    is_int(sK14(pls,pls,m)),
    inference(superposition,[status(thm)],[c_76363,c_90022]) ).

tcf(c_90030,plain,
    is_int(sK14(m,pls,m)),
    inference(superposition,[status(thm)],[c_76934,c_90022]) ).

tcf(c_90033,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,X1),pls,m)),X0)) = sK14(hAPP_int_int(iPr_def_13,X1),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_46106]) ).

tcf(c_90034,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,X1),pls,m))),X0) = pls,
    inference(superposition,[status(thm)],[c_90022,c_46104]) ).

tcf(c_90035,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)),pls) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_880]) ).

tcf(c_90036,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_608]) ).

tcf(c_90037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)),pls) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_524]) ).

tcf(c_90038,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,X0),pls,m)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_523]) ).

tcf(c_90039,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,X0),pls,m)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_347]) ).

tcf(c_90040,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)),one_one_int) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_346]) ).

tcf(c_90041,plain,
    ! [X0: $i] : number_number_of_int(sK14(hAPP_int_int(iPr_def_13,X0),pls,m)) = sK14(hAPP_int_int(iPr_def_13,X0),pls,m),
    inference(superposition,[status(thm)],[c_90022,c_254]) ).

tcf(c_90101,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88519,c_1042]) ).

tcf(c_90102,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88519,c_833]) ).

tcf(c_90104,plain,
    ! [X0: $i] : hBOOL(member_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_88519,c_76535]) ).

tcf(c_90105,plain,
    ! [X0: $i] : hBOOL(member_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88519,c_76498]) ).

tcf(c_90106,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88519,c_1045]) ).

tcf(c_90107,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88519,c_833]) ).

tcf(c_90108,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_88519,c_88514]) ).

tcf(c_90109,plain,
    hAPP_int_int(div_mod_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_88519,c_88551]) ).

tcf(c_90119,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls))),
    inference(superposition,[status(thm)],[c_574,c_83514]) ).

tcf(c_90120,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min))),
    inference(superposition,[status(thm)],[c_76397,c_83514]) ).

tcf(c_90121,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_83514]) ).

tcf(c_90122,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_83514]) ).

tcf(c_90123,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0)))),
    inference(superposition,[status(thm)],[c_76399,c_83514]) ).

tcf(c_90124,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1)))),
    inference(superposition,[status(thm)],[c_76401,c_83514]) ).

tcf(c_90125,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))),
    inference(superposition,[status(thm)],[c_76402,c_83514]) ).

tcf(c_90126,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1))),
    inference(superposition,[status(thm)],[c_76403,c_83514]) ).

tcf(c_90127,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s))),
    inference(superposition,[status(thm)],[c_76404,c_83514]) ).

tcf(c_90128,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t))),
    inference(superposition,[status(thm)],[c_76405,c_83514]) ).

tcf(c_90129,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_83514]) ).

tcf(c_90130,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_83514]) ).

tcf(c_90131,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_83514]) ).

tcf(c_90132,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_83514]) ).

tcf(c_90133,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_83514]) ).

tcf(c_90134,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_83514]) ).

tcf(c_90135,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_83514]) ).

tcf(c_90136,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_83514]) ).

tcf(c_90137,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_83514]) ).

tcf(c_90139,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))),
    inference(superposition,[status(thm)],[c_77366,c_83514]) ).

tcf(c_90140,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_83514]) ).

tcf(c_90142,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79414,c_83514]) ).

tcf(c_90144,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_83514]) ).

tcf(c_90146,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79931,c_83514]) ).

tcf(c_90147,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_83504,c_83514]) ).

tcf(c_90148,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79957,c_83514]) ).

tcf(c_90149,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80664,c_83514]) ).

tcf(c_90150,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80677,c_83514]) ).

tcf(c_90151,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),
    inference(superposition,[status(thm)],[c_80692,c_83514]) ).

tcf(c_90152,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_83514]) ).

tcf(c_90153,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_83514]) ).

tcf(c_90154,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_83514]) ).

tcf(c_90155,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_83514]) ).

tcf(c_90158,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_90125,c_79190]) ).

tcf(c_90226,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(sK27(X1,X0),hAPP_i1948725293t_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46406,c_226]) ).

tcf(c_90263,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X0,zcong(X1,sK27(X1,X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46408,c_226]) ).

tcf(c_90264,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(X1,sK27(X1,X0),X0))
      | ~ is_int(sK27(X1,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46408,c_852]) ).

tcf(c_90265,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK27(X1,X0),X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46408,c_814]) ).

tcf(c_90286,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(sK27(X1,X0),cOMBC_int_int_bool(ord_less_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46414,c_226]) ).

tcf(c_90293,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(pls))) ),
    inference(superposition,[status(thm)],[c_786,c_131]) ).

tcf(c_90294,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(min))) ),
    inference(superposition,[status(thm)],[c_78282,c_131]) ).

tcf(c_90295,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78547,c_131]) ).

tcf(c_90296,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(pls)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_786,c_131]) ).

tcf(c_90297,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(min)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78282,c_131]) ).

tcf(c_90298,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),iPr_def_11))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(iPr_def_14)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78547,c_131]) ).

tcf(c_90299,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(pls))) ),
    inference(superposition,[status(thm)],[c_786,c_131]) ).

tcf(c_90300,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(min))) ),
    inference(superposition,[status(thm)],[c_78282,c_131]) ).

tcf(c_90301,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,iPr_def_11),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78547,c_131]) ).

tcf(c_90302,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(pls)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_786,c_131]) ).

tcf(c_90303,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(min)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78282,c_131]) ).

tcf(c_90304,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),iPr_def_11))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(iPr_def_14)),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78547,c_131]) ).

tcf(c_90305,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ( hAPP_nat_nat(div_mod_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(X0) ) ),
    inference(superposition,[status(thm)],[c_131,c_1693]) ).

tcf(c_90306,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(superposition,[status(thm)],[c_131,c_1364]) ).

tcf(c_90307,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(superposition,[status(thm)],[c_131,c_594]) ).

tcf(c_90308,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X0))),
    inference(superposition,[status(thm)],[c_131,c_1358]) ).

tcf(c_90310,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ( hAPP_nat_nat(minus_minus_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_131,c_1332]) ).

tcf(c_90314,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),iPr_def_11)) ),
    inference(light_normalisation,[status(thm)],[c_90304,c_78547]) ).

tcf(c_90317,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(light_normalisation,[status(thm)],[c_90303,c_78282]) ).

tcf(c_90321,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,iPr_def_11),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),iPr_def_11)) ),
    inference(light_normalisation,[status(thm)],[c_90301,c_78547]) ).

tcf(c_90324,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),number_number_of_nat(X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(light_normalisation,[status(thm)],[c_90300,c_78282]) ).

tcf(c_90353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,pls,m)),X0)) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_46106]) ).

tcf(c_90354,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,pls,m))),X0) = pls,
    inference(superposition,[status(thm)],[c_90029,c_46104]) ).

tcf(c_90355,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,pls,m)),pls) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_880]) ).

tcf(c_90356,plain,
    hAPP_nat_int(power_power_int(sK14(pls,pls,m)),one_one_nat) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_608]) ).

tcf(c_90357,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,pls,m)),pls) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_524]) ).

tcf(c_90358,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,pls,m)) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_523]) ).

tcf(c_90359,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,pls,m)) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_347]) ).

tcf(c_90360,plain,
    hAPP_int_int(times_times_int(sK14(pls,pls,m)),one_one_int) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_346]) ).

tcf(c_90361,plain,
    number_number_of_int(sK14(pls,pls,m)) = sK14(pls,pls,m),
    inference(superposition,[status(thm)],[c_90029,c_254]) ).

tcf(c_90414,plain,
    hBOOL(member_int(one_one_int,zcong(m,pls))),
    inference(superposition,[status(thm)],[c_76934,c_85182]) ).

tcf(c_90415,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),pls))),
    inference(superposition,[status(thm)],[c_79319,c_85182]) ).

tcf(c_90416,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))),zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),pls))),
    inference(superposition,[status(thm)],[c_79319,c_85182]) ).

tcf(c_90418,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),zcong(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),pls))),
    inference(light_normalisation,[status(thm)],[c_90415,c_79321]) ).

tcf(c_90446,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88556,c_1042]) ).

tcf(c_90447,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88556,c_833]) ).

tcf(c_90449,plain,
    ! [X0: $i] : hBOOL(member_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_88556,c_76535]) ).

tcf(c_90450,plain,
    ! [X0: $i] : hBOOL(member_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88556,c_76498]) ).

tcf(c_90451,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88556,c_1045]) ).

tcf(c_90452,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88556,c_833]) ).

tcf(c_90454,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_88556,c_88551]) ).

tcf(c_90457,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int)) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_59636,c_88494]) ).

tcf(c_90461,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = number_number_of_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88494,c_79918]) ).

tcf(c_90462,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = number_number_of_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88494,c_79931]) ).

tcf(c_90463,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90461,c_88502]) ).

tcf(c_90464,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90462,c_88502]) ).

tcf(c_90465,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int)) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_59636,c_88513]) ).

tcf(c_90467,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_88552,c_88513]) ).

tcf(c_90477,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88513,c_76880]) ).

tcf(c_90478,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = number_number_of_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88513,c_79918]) ).

tcf(c_90479,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = number_number_of_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88513,c_79931]) ).

tcf(c_90480,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90478,c_88521]) ).

tcf(c_90481,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90479,c_88521]) ).

tcf(c_90485,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int)) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_59636,c_88550]) ).

tcf(c_90495,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88550,c_76880]) ).

tcf(c_90496,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = number_number_of_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88550,c_79918]) ).

tcf(c_90497,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = number_number_of_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88550,c_79931]) ).

tcf(c_90498,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90496,c_88558]) ).

tcf(c_90499,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))) = sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_90497,c_88558]) ).

tcf(c_90503,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls))),
    inference(superposition,[status(thm)],[c_574,c_83515]) ).

tcf(c_90504,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min))),
    inference(superposition,[status(thm)],[c_76397,c_83515]) ).

tcf(c_90505,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_83515]) ).

tcf(c_90506,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_83515]) ).

tcf(c_90507,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0)))),
    inference(superposition,[status(thm)],[c_76399,c_83515]) ).

tcf(c_90508,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1)))),
    inference(superposition,[status(thm)],[c_76401,c_83515]) ).

tcf(c_90509,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))),
    inference(superposition,[status(thm)],[c_76402,c_83515]) ).

tcf(c_90510,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1))),
    inference(superposition,[status(thm)],[c_76403,c_83515]) ).

tcf(c_90511,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s))),
    inference(superposition,[status(thm)],[c_76404,c_83515]) ).

tcf(c_90512,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t))),
    inference(superposition,[status(thm)],[c_76405,c_83515]) ).

tcf(c_90513,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_83515]) ).

tcf(c_90514,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_83515]) ).

tcf(c_90515,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_83515]) ).

tcf(c_90516,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_83515]) ).

tcf(c_90517,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_83515]) ).

tcf(c_90518,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_83515]) ).

tcf(c_90519,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_83515]) ).

tcf(c_90520,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_83515]) ).

tcf(c_90521,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_83515]) ).

tcf(c_90523,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))),
    inference(superposition,[status(thm)],[c_77366,c_83515]) ).

tcf(c_90524,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_83515]) ).

tcf(c_90526,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79414,c_83515]) ).

tcf(c_90528,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_83515]) ).

tcf(c_90530,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79931,c_83515]) ).

tcf(c_90531,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_83504,c_83515]) ).

tcf(c_90532,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79957,c_83515]) ).

tcf(c_90533,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80664,c_83515]) ).

tcf(c_90534,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80677,c_83515]) ).

tcf(c_90535,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),
    inference(superposition,[status(thm)],[c_80692,c_83515]) ).

tcf(c_90536,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_83515]) ).

tcf(c_90537,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_83515]) ).

tcf(c_90538,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_83515]) ).

tcf(c_90539,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_83515]) ).

tcf(c_90540,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))),
    inference(superposition,[status(thm)],[c_83515,c_80436]) ).

tcf(c_90544,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_90509,c_79190]) ).

tcf(c_90614,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(light_normalisation,[status(thm)],[c_193,c_76874]) ).

tcf(c_90621,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X1),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_90614]) ).

tcf(c_90622,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_59638,c_90614]) ).

tcf(c_90623,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_15),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),X0)) ),
    inference(superposition,[status(thm)],[c_59639,c_90614]) ).

tcf(c_90624,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_16),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),X0)) ),
    inference(superposition,[status(thm)],[c_59640,c_90614]) ).

tcf(c_90625,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_18),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),X0)) ),
    inference(superposition,[status(thm)],[c_59642,c_90614]) ).

tcf(c_90626,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(min),min)),X0)) ),
    inference(superposition,[status(thm)],[c_76610,c_90614]) ).

tcf(c_90628,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)),X0)) ),
    inference(superposition,[status(thm)],[c_82935,c_90614]) ).

tcf(c_90629,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK30(iPr_def_19)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),X0)) ),
    inference(superposition,[status(thm)],[c_83830,c_90614]) ).

tcf(c_90630,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(X1,hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_90614,c_226]) ).

tcf(c_90631,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(iPr_def_12,X0))) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_90614,c_46168]) ).

tcf(c_90632,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(hAPP_int_int(iPr_def_12,X0))) = one_one_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_90614,c_46166]) ).

tcf(c_90633,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(iPr_def_12,X0))) = one_one_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_90614,c_46164]) ).

tcf(c_90634,plain,
    ! [X0: $i] :
      ( ( zfact(hAPP_int_int(iPr_def_12,X0)) = one_one_int )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_90614,c_1519]) ).

tcf(c_90635,plain,
    ! [X0: $i] :
      ( ( number_number_of_nat(hAPP_int_int(iPr_def_12,X0)) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_90614,c_811]) ).

tcf(c_90636,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK30(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0))))) ),
    inference(superposition,[status(thm)],[c_90614,c_1561]) ).

tcf(c_90637,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP3(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK39(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1,X2))) ),
    inference(superposition,[status(thm)],[c_90614,c_1647]) ).

tcf(c_90645,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),X0))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_90622,c_59643]) ).

tcf(c_90699,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1)) ),
    inference(light_normalisation,[status(thm)],[c_194,c_76874]) ).

tcf(c_90706,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_12,X0))),
    inference(superposition,[status(thm)],[c_114,c_90699]) ).

tcf(c_90707,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)))) ),
    inference(superposition,[status(thm)],[c_1563,c_90699]) ).

tcf(c_90708,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_12,X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79141,c_90699]) ).

tcf(c_90710,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X0),hAPP_int_int(iPr_def_12,X1))) ),
    inference(superposition,[status(thm)],[c_1720,c_90699]) ).

tcf(c_90711,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),X0)) ),
    inference(superposition,[status(thm)],[c_59638,c_90699]) ).

tcf(c_90712,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_15),X0)) ),
    inference(superposition,[status(thm)],[c_59639,c_90699]) ).

tcf(c_90713,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_16),X0)) ),
    inference(superposition,[status(thm)],[c_59640,c_90699]) ).

tcf(c_90714,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_17),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_18),X0)) ),
    inference(superposition,[status(thm)],[c_59642,c_90699]) ).

tcf(c_90715,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(min),min)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_76610,c_90699]) ).

tcf(c_90717,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),X0)) ),
    inference(superposition,[status(thm)],[c_82935,c_90699]) ).

tcf(c_90718,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK30(iPr_def_19)),X0)) ),
    inference(superposition,[status(thm)],[c_83830,c_90699]) ).

tcf(c_90725,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),X0)) ),
    inference(light_normalisation,[status(thm)],[c_90711,c_59643]) ).

tcf(c_90800,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(X1),hAPP_nat_int(power_power_int(X0),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_217]) ).

tcf(c_90801,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X0)),
    inference(superposition,[status(thm)],[c_253,c_217]) ).

tcf(c_90805,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(X0),pls),
    inference(superposition,[status(thm)],[c_1004,c_217]) ).

tcf(c_90806,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(X1),number_number_of_int(X2))) = hAPP_int_int(times_times_int(X1),number_number_of_int(hAPP_int_int(times_times_int(X0),X2))),
    inference(superposition,[status(thm)],[c_382,c_217]) ).

tcf(c_90807,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),pls)) = hAPP_int_int(times_times_int(X1),pls),
    inference(superposition,[status(thm)],[c_1001,c_217]) ).

tcf(c_90808,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(X0),min)) = hAPP_int_int(times_times_int(X0),one_one_int),
    inference(superposition,[status(thm)],[c_79464,c_217]) ).

tcf(c_90809,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),m)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_13,X0)),
    inference(superposition,[status(thm)],[c_76855,c_217]) ).

tcf(c_90810,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(X0),one_one_int)) = hAPP_int_int(times_times_int(X0),iPr_def_15),
    inference(superposition,[status(thm)],[c_76925,c_217]) ).

tcf(c_90811,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(X0),one_one_int)) = hAPP_int_int(times_times_int(X0),iPr_def_16),
    inference(superposition,[status(thm)],[c_76926,c_217]) ).

tcf(c_90812,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(X0),one_one_int)) = hAPP_int_int(times_times_int(X0),iPr_def_17),
    inference(superposition,[status(thm)],[c_76927,c_217]) ).

tcf(c_90813,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(X0),one_one_int)) = hAPP_int_int(times_times_int(X0),iPr_def_18),
    inference(superposition,[status(thm)],[c_76928,c_217]) ).

tcf(c_90814,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_76995,c_217]) ).

tcf(c_90815,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),undefined_int(int))) = hAPP_int_int(times_times_int(X0),undefined_int(int)),
    inference(superposition,[status(thm)],[c_77063,c_217]) ).

tcf(c_90816,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),twoSqu1241645765sum2sq(X1))) = hAPP_int_int(times_times_int(X0),twoSqu1241645765sum2sq(X1)),
    inference(superposition,[status(thm)],[c_77069,c_217]) ).

tcf(c_90817,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_79150,c_217]) ).

tcf(c_90818,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X2)))) = hAPP_int_int(times_times_int(X1),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2)))),
    inference(superposition,[status(thm)],[c_79563,c_217]) ).

tcf(c_90819,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80257,c_217]) ).

tcf(c_90820,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_80257,c_217]) ).

tcf(c_90821,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80428,c_217]) ).

tcf(c_90822,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_80531,c_217]) ).

tcf(c_90823,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X1))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_82021,c_217]) ).

tcf(c_90824,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88500,c_217]) ).

tcf(c_90825,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88519,c_217]) ).

tcf(c_90826,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88556,c_217]) ).

tcf(c_90827,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,X1)) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_59637,c_217]) ).

tcf(c_90895,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X2),X1)))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_217,c_65]) ).

tcf(c_90896,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_int_int(times_times_int(X2),X2)))),
    inference(superposition,[status(thm)],[c_217,c_584]) ).

tcf(c_90897,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82916]) ).

tcf(c_90898,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_83500]) ).

tcf(c_90899,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82917]) ).

tcf(c_90900,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_83274]) ).

tcf(c_90901,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82913]) ).

tcf(c_90902,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82918]) ).

tcf(c_90903,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),
    inference(superposition,[status(thm)],[c_217,c_82909]) ).

tcf(c_90904,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_217,c_82861]) ).

tcf(c_90905,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_217,c_11305]) ).

tcf(c_90906,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1)),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_217,c_76545]) ).

tcf(c_90907,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_217,c_1135]) ).

tcf(c_90909,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X2),X1)))),
    inference(superposition,[status(thm)],[c_217,c_1042]) ).

tcf(c_90910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X3),hAPP_int_int(times_times_int(X0),X2))),hAPP_int_int(times_times_int(X0),X2))),
    inference(superposition,[status(thm)],[c_217,c_833]) ).

tcf(c_90911,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_217,c_76863]) ).

tcf(c_90912,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X2),X1)),
    inference(superposition,[status(thm)],[c_217,c_253]) ).

tcf(c_90913,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_i1948725293t_bool(dvd_dvd_int,X1))),
    inference(superposition,[status(thm)],[c_217,c_76535]) ).

tcf(c_90914,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X2)))),
    inference(superposition,[status(thm)],[c_217,c_76498]) ).

tcf(c_90915,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)))),
    inference(superposition,[status(thm)],[c_217,c_1045]) ).

tcf(c_90916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X3))) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X0),X3))),
    inference(superposition,[status(thm)],[c_217,c_217]) ).

tcf(c_90918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X3),X2))),hAPP_int_int(times_times_int(X1),X2))),
    inference(superposition,[status(thm)],[c_217,c_833]) ).

tcf(c_90919,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(pls),X1)) = pls,
    inference(superposition,[status(thm)],[c_217,c_1004]) ).

tcf(c_90920,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),X2))))),
    inference(superposition,[status(thm)],[c_217,c_584]) ).

tcf(c_90921,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_83274]) ).

tcf(c_90922,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82919]) ).

tcf(c_90923,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X2),X2)),X1))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X2),X2))),hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_217,c_78759]) ).

tcf(c_90924,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88519]) ).

tcf(c_90925,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88518]) ).

tcf(c_90926,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88516]) ).

tcf(c_90927,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88515]) ).

tcf(c_90928,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_217,c_89604]) ).

tcf(c_90929,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88521]) ).

tcf(c_90930,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_88319]) ).

tcf(c_90931,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),pls),hAPP_int_int(times_times_int(X0),X1))),
    inference(superposition,[status(thm)],[c_217,c_84092]) ).

tcf(c_90932,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),X1),zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),pls))),
    inference(superposition,[status(thm)],[c_217,c_84084]) ).

tcf(c_90933,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_217,c_83484]) ).

tcf(c_90934,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_217,c_79573]) ).

tcf(c_90935,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_217,c_79414]) ).

tcf(c_90936,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_217,c_78432]) ).

tcf(c_90937,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_217,c_78420]) ).

tcf(c_90938,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_78405]) ).

tcf(c_90939,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_78397]) ).

tcf(c_90940,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)) != min,
    inference(superposition,[status(thm)],[c_217,c_79170]) ).

tcf(c_90941,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)))),
    inference(superposition,[status(thm)],[c_217,c_79161]) ).

tcf(c_90942,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)) != iPr_def_15,
    inference(superposition,[status(thm)],[c_217,c_79169]) ).

tcf(c_90943,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)) != one_one_int,
    inference(superposition,[status(thm)],[c_217,c_79165]) ).

tcf(c_90944,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)))),
    inference(superposition,[status(thm)],[c_217,c_79163]) ).

tcf(c_90945,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),
    inference(superposition,[status(thm)],[c_217,c_79216]) ).

tcf(c_90946,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_217,c_79563]) ).

tcf(c_90947,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_217,c_88513]) ).

tcf(c_90948,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2)),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_88514]) ).

tcf(c_90949,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_80428]) ).

tcf(c_90950,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_80427]) ).

tcf(c_90951,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_80425]) ).

tcf(c_90952,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_80424]) ).

tcf(c_90953,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_217,c_80313]) ).

tcf(c_90955,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_83642]) ).

tcf(c_90956,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_83009]) ).

tcf(c_90957,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_217,c_80400]) ).

tcf(c_90958,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_83009]) ).

tcf(c_90959,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_82913]) ).

tcf(c_90960,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_83008]) ).

tcf(c_90961,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_85345]) ).

tcf(c_90964,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(light_normalisation,[status(thm)],[c_90805,c_1001]) ).

tcf(c_90967,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(light_normalisation,[status(thm)],[c_90946,c_79448]) ).

tcf(c_90968,plain,
    hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),m)) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_83481,c_90827]) ).

tcf(c_90969,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),
    inference(demodulation,[status(thm)],[c_80435,c_90827]) ).

tcf(c_90970,plain,
    is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_80431,c_90827]) ).

tcf(c_90975,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(X0)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_82021,c_90800]) ).

tcf(c_90977,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80257,c_90800]) ).

tcf(c_90978,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80400,c_90800]) ).

tcf(c_90979,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_83642,c_90800]) ).

tcf(c_90980,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(demodulation,[status(thm)],[c_83009,c_90800]) ).

tcf(c_90981,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80531,c_90977]) ).

tcf(c_90982,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80530,c_90977]) ).

tcf(c_90983,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_nat) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80528,c_90977]) ).

tcf(c_90984,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_80527,c_90977]) ).

tcf(c_90985,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_80314,c_90977]) ).

tcf(c_91227,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X0)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82316,c_218]) ).

tcf(c_91231,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0)),
    inference(superposition,[status(thm)],[c_1309,c_218]) ).

tcf(c_91232,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),one_one_nat)) = hAPP_nat_nat(times_times_nat(X1),X0),
    inference(superposition,[status(thm)],[c_1413,c_218]) ).

tcf(c_91233,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(one_one_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(times_times_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1417,c_218]) ).

tcf(c_91234,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(times_times_nat(X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1336,c_218]) ).

tcf(c_91235,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat)) = hAPP_nat_nat(times_times_nat(X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1337,c_218]) ).

tcf(c_91257,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_218,c_82316]) ).

tcf(c_91258,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1))))),
    inference(superposition,[status(thm)],[c_218,c_1408]) ).

tcf(c_91260,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_218,c_1409]) ).

tcf(c_91262,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X2) = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_218,c_1416]) ).

tcf(c_91263,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_218,c_1415]) ).

tcf(c_91264,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X1) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_218,c_1684]) ).

tcf(c_91268,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2)))),
    inference(superposition,[status(thm)],[c_218,c_1044]) ).

tcf(c_91269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X3))) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X0),X3))),
    inference(superposition,[status(thm)],[c_218,c_218]) ).

tcf(c_91270,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X2),X1)),
    inference(superposition,[status(thm)],[c_218,c_1309]) ).

tcf(c_91271,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X2),X1)))),
    inference(superposition,[status(thm)],[c_218,c_1041]) ).

tcf(c_91272,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_nat(times_times_nat(X0),X1),
    inference(superposition,[status(thm)],[c_218,c_1417]) ).

tcf(c_91273,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(zero_zero_nat),X1)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_218,c_1336]) ).

tcf(c_91274,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) = one_one_real,
    inference(superposition,[status(thm)],[c_218,c_85145]) ).

tcf(c_91275,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) = one_one_int,
    inference(superposition,[status(thm)],[c_218,c_85131]) ).

tcf(c_91276,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))))),
    inference(superposition,[status(thm)],[c_218,c_89096]) ).

tcf(c_91277,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))))),
    inference(superposition,[status(thm)],[c_218,c_88797]) ).

tcf(c_91278,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_91234,c_1337]) ).

tcf(c_91320,plain,
    hBOOL(hAPP_int_bool(zcong(pls,m),one_one_int)),
    inference(superposition,[status(thm)],[c_76934,c_85183]) ).

tcf(c_91321,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_85183]) ).

tcf(c_91322,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_85183]) ).

tcf(c_91323,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(pls,hAPP_int_int(iPr_def_13,X0)))),
    inference(superposition,[status(thm)],[c_85183,c_226]) ).

tcf(c_91324,plain,
    ! [X0: $i] :
      ( is_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0))
      | ~ is_int(hAPP_int_int(iPr_def_13,X0)) ),
    inference(superposition,[status(thm)],[c_85183,c_852]) ).

tcf(c_91326,plain,
    ! [X0: $i] : is_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_91324,c_77054]) ).

tcf(c_91327,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_91321,c_79321]) ).

tcf(c_91346,plain,
    is_int(sK14(pls,m,one_one_int)),
    inference(superposition,[status(thm)],[c_76934,c_91326]) ).

tcf(c_91347,plain,
    ! [X0: $i] : is_int(sK14(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79319,c_91326]) ).

tcf(c_91348,plain,
    ! [X0: $i] : is_int(sK14(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))),
    inference(superposition,[status(thm)],[c_79319,c_91326]) ).

tcf(c_91349,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,hAPP_int_int(iPr_def_13,X1),X1)),X0)) = sK14(pls,hAPP_int_int(iPr_def_13,X1),X1),
    inference(superposition,[status(thm)],[c_91326,c_46106]) ).

tcf(c_91350,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,hAPP_int_int(iPr_def_13,X1),X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_91326,c_46104]) ).

tcf(c_91351,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)),pls) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_880]) ).

tcf(c_91352,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)),one_one_nat) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_608]) ).

tcf(c_91353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)),pls) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_524]) ).

tcf(c_91354,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_523]) ).

tcf(c_91355,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_347]) ).

tcf(c_91356,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)),one_one_int) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_346]) ).

tcf(c_91357,plain,
    ! [X0: $i] : number_number_of_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),X0)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),X0),
    inference(superposition,[status(thm)],[c_91326,c_254]) ).

tcf(c_91358,plain,
    ! [X0: $i] : is_int(sK14(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_91347,c_79321]) ).

tcf(c_91390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,m,one_one_int)),X0)) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_46106]) ).

tcf(c_91391,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,m,one_one_int))),X0) = pls,
    inference(superposition,[status(thm)],[c_91346,c_46104]) ).

tcf(c_91392,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,m,one_one_int)),pls) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_880]) ).

tcf(c_91393,plain,
    hAPP_nat_int(power_power_int(sK14(pls,m,one_one_int)),one_one_nat) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_608]) ).

tcf(c_91394,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,m,one_one_int)),pls) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_524]) ).

tcf(c_91395,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,m,one_one_int)) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_523]) ).

tcf(c_91396,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,m,one_one_int)) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_347]) ).

tcf(c_91397,plain,
    hAPP_int_int(times_times_int(sK14(pls,m,one_one_int)),one_one_int) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_346]) ).

tcf(c_91398,plain,
    number_number_of_int(sK14(pls,m,one_one_int)) = sK14(pls,m,one_one_int),
    inference(superposition,[status(thm)],[c_91346,c_254]) ).

tcf(c_91423,plain,
    legendre(m,one_one_int) = pls,
    inference(superposition,[status(thm)],[c_76934,c_85185]) ).

tcf(c_91424,plain,
    ! [X0: $i] : legendre(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) = pls,
    inference(superposition,[status(thm)],[c_79319,c_85185]) ).

tcf(c_91425,plain,
    ! [X0: $i] : legendre(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0)))) = pls,
    inference(superposition,[status(thm)],[c_79319,c_85185]) ).

tcf(c_91427,plain,
    ! [X0: $i] : legendre(hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))) = pls,
    inference(light_normalisation,[status(thm)],[c_91424,c_79321]) ).

tcf(c_91430,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_90902,c_90904]) ).

tcf(c_91431,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X1),X2)),iPr_def_11)) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_90922,c_90904]) ).

tcf(c_91432,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_253,c_90985]) ).

tcf(c_91434,plain,
    is_int(hAPP_int_int(times_times_int(pls),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_574,c_90985]) ).

tcf(c_91436,plain,
    is_int(hAPP_int_int(times_times_int(one_one_int),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76393,c_90985]) ).

tcf(c_91437,plain,
    is_int(hAPP_int_int(times_times_int(undefined_int(int)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76395,c_90985]) ).

tcf(c_91439,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76401,c_90985]) ).

tcf(c_91440,plain,
    is_int(hAPP_int_int(times_times_int(m),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76402,c_90985]) ).

tcf(c_91448,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76410,c_90985]) ).

tcf(c_91454,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_77366,c_90985]) ).

tcf(c_91455,plain,
    is_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78203,c_90985]) ).

tcf(c_91457,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79414,c_90985]) ).

tcf(c_91459,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79437,c_90985]) ).

tcf(c_91461,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79931,c_90985]) ).

tcf(c_91462,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_83504,c_90985]) ).

tcf(c_91463,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79957,c_90985]) ).

tcf(c_91464,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_80664,c_90985]) ).

tcf(c_91465,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_80677,c_90985]) ).

tcf(c_91466,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_80692,c_90985]) ).

tcf(c_91467,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_80705,c_90985]) ).

tcf(c_91468,plain,
    is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88502,c_90985]) ).

tcf(c_91469,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88521,c_90985]) ).

tcf(c_91470,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88558,c_90985]) ).

tcf(c_91475,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_90985,c_524]) ).

tcf(c_91478,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_int) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_90985,c_346]) ).

tcf(c_91479,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_90985,c_254]) ).

tcf(c_91480,plain,
    is_int(hAPP_int_int(iPr_def_13,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_91440,c_59637]) ).

tcf(c_91523,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_253,c_90959]) ).

tcf(c_91525,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_90959]) ).

tcf(c_91527,plain,
    hAPP_int_int(times_times_int(pls),pls) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_90959]) ).

tcf(c_91528,plain,
    hAPP_int_int(times_times_int(m),hAPP_int_int(iPr_def_13,iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_76855,c_90959]) ).

tcf(c_91529,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_90959]) ).

tcf(c_91530,plain,
    hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_91528,c_59637]) ).

tcf(c_91534,plain,
    ! [X0: $i] : is_int(sK14(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),iPr_def_11),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_90930]) ).

tcf(c_91535,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_253,c_90930]) ).

tcf(c_91537,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_90930]) ).

tcf(c_91540,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_59637,c_90930]) ).

tcf(c_91541,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_82861,c_90930]) ).

tcf(c_91542,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_253,c_90930]) ).

tcf(c_91544,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_217,c_90930]) ).

tcf(c_91546,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),pls),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_1001,c_90930]) ).

tcf(c_91547,plain,
    ! [X0: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76855,c_90930]) ).

tcf(c_91552,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_90930,c_524]) ).

tcf(c_91555,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_int) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_90930,c_346]) ).

tcf(c_91567,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_90901,c_90904]) ).

tcf(c_91568,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_90900,c_90904]) ).

tcf(c_91569,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls))),
    inference(superposition,[status(thm)],[c_574,c_83516]) ).

tcf(c_91570,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min))),
    inference(superposition,[status(thm)],[c_76397,c_83516]) ).

tcf(c_91571,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_83516]) ).

tcf(c_91572,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_83516]) ).

tcf(c_91573,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0)))),
    inference(superposition,[status(thm)],[c_76399,c_83516]) ).

tcf(c_91574,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1)))),
    inference(superposition,[status(thm)],[c_76401,c_83516]) ).

tcf(c_91575,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))),
    inference(superposition,[status(thm)],[c_76402,c_83516]) ).

tcf(c_91576,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1))),
    inference(superposition,[status(thm)],[c_76403,c_83516]) ).

tcf(c_91577,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s))),
    inference(superposition,[status(thm)],[c_76404,c_83516]) ).

tcf(c_91578,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t))),
    inference(superposition,[status(thm)],[c_76405,c_83516]) ).

tcf(c_91579,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_83516]) ).

tcf(c_91580,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_83516]) ).

tcf(c_91581,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_83516]) ).

tcf(c_91582,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_83516]) ).

tcf(c_91583,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_83516]) ).

tcf(c_91584,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_83516]) ).

tcf(c_91585,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_83516]) ).

tcf(c_91586,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_83516]) ).

tcf(c_91587,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_83516]) ).

tcf(c_91589,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))),
    inference(superposition,[status(thm)],[c_77366,c_83516]) ).

tcf(c_91590,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_83516]) ).

tcf(c_91592,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79414,c_83516]) ).

tcf(c_91594,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_83516]) ).

tcf(c_91596,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_79931,c_83516]) ).

tcf(c_91597,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_83504,c_83516]) ).

tcf(c_91598,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79957,c_83516]) ).

tcf(c_91599,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80664,c_83516]) ).

tcf(c_91600,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_80677,c_83516]) ).

tcf(c_91601,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),
    inference(superposition,[status(thm)],[c_80692,c_83516]) ).

tcf(c_91602,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_83516]) ).

tcf(c_91603,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_83516]) ).

tcf(c_91604,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_83516]) ).

tcf(c_91605,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_83516]) ).

tcf(c_91607,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_91575,c_79190]) ).

tcf(c_91702,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(X1),hAPP_nat_real(power_power_real(X0),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82839,c_219]) ).

tcf(c_91706,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),X0)),
    inference(superposition,[status(thm)],[c_976,c_219]) ).

tcf(c_91707,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),one_one_real)) = hAPP_real_real(times_times_real(X1),X0),
    inference(superposition,[status(thm)],[c_325,c_219]) ).

tcf(c_91708,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(one_one_real),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(X0),X1),
    inference(superposition,[status(thm)],[c_977,c_219]) ).

tcf(c_91709,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),X1)),
    inference(superposition,[status(thm)],[c_373,c_219]) ).

tcf(c_91710,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(number267125858f_real(X0)),hAPP_real_real(times_times_real(X1),number267125858f_real(X2))) = hAPP_real_real(times_times_real(X1),number267125858f_real(hAPP_int_int(times_times_int(X0),X2))),
    inference(superposition,[status(thm)],[c_383,c_219]) ).

tcf(c_91711,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),number267125858f_real(X1))) = hAPP_real_real(times_times_real(X0),number267125858f_real(hAPP_int_int(plus_plus_int(X1),X1))),
    inference(superposition,[status(thm)],[c_408,c_219]) ).

tcf(c_91712,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(zero_zero_real),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(X0),zero_zero_real),
    inference(superposition,[status(thm)],[c_1002,c_219]) ).

tcf(c_91713,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),zero_zero_real)) = hAPP_real_real(times_times_real(X1),zero_zero_real),
    inference(superposition,[status(thm)],[c_999,c_219]) ).

tcf(c_91714,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))) = hAPP_real_real(times_times_real(X1),hAPP_real_real(plus_plus_real(X0),X0)),
    inference(superposition,[status(thm)],[c_14792,c_219]) ).

tcf(c_91729,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1))),hAPP_real_real(times_times_real(X2),X2)))),
    inference(superposition,[status(thm)],[c_219,c_585]) ).

tcf(c_91730,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1)) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_219,c_82839]) ).

tcf(c_91731,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1))))
      | ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_219,c_759]) ).

tcf(c_91732,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_219,c_1201]) ).

tcf(c_91733,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_219,c_1134]) ).

tcf(c_91735,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X2)))),
    inference(superposition,[status(thm)],[c_219,c_1043]) ).

tcf(c_91736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),X3))) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X0),X3))),
    inference(superposition,[status(thm)],[c_219,c_219]) ).

tcf(c_91738,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X2),X1)),
    inference(superposition,[status(thm)],[c_219,c_976]) ).

tcf(c_91739,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X2),X1)))),
    inference(superposition,[status(thm)],[c_219,c_1040]) ).

tcf(c_91740,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(one_one_real),X1)) = hAPP_real_real(times_times_real(X0),X1),
    inference(superposition,[status(thm)],[c_219,c_977]) ).

tcf(c_91741,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(zero_zero_real),X1)) = zero_zero_real,
    inference(superposition,[status(thm)],[c_219,c_1002]) ).

tcf(c_91742,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X1),X2)),X2))))),
    inference(superposition,[status(thm)],[c_219,c_585]) ).

tcf(c_91743,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(zero_zero_real),hAPP_real_real(times_times_real(X0),X1)) = zero_zero_real,
    inference(light_normalisation,[status(thm)],[c_91712,c_999]) ).

tcf(c_91791,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X2)),
    inference(superposition,[status(thm)],[c_243,c_237]) ).

tcf(c_91792,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),X1) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_14792,c_237]) ).

tcf(c_91793,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0)),X1) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_373,c_237]) ).

tcf(c_91795,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(zero_zero_real),hAPP_real_real(plus_plus_real(X0),X1)) = hAPP_real_real(plus_plus_real(X0),X1),
    inference(superposition,[status(thm)],[c_508,c_237]) ).

tcf(c_91796,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(zero_zero_real),X1)) = hAPP_real_real(plus_plus_real(X0),X1),
    inference(superposition,[status(thm)],[c_516,c_237]) ).

tcf(c_91797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2))),X3) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X2),X3)),
    inference(superposition,[status(thm)],[c_237,c_237]) ).

tcf(c_91798,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) != hAPP_real_real(plus_plus_real(X0),X1) ) ),
    inference(superposition,[status(thm)],[c_237,c_517]) ).

tcf(c_91799,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X0)),
    inference(superposition,[status(thm)],[c_237,c_243]) ).

tcf(c_91801,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),
    inference(superposition,[status(thm)],[c_237,c_14792]) ).

tcf(c_91802,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_237,c_373]) ).

tcf(c_91803,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(plus_plus_real(X0),X1) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1))) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_237,c_521]) ).

tcf(c_91804,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),zero_zero_real)) = hAPP_real_real(plus_plus_real(X0),X1),
    inference(superposition,[status(thm)],[c_237,c_516]) ).

tcf(c_91866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X3))),
    inference(superposition,[status(thm)],[c_237,c_240]) ).

tcf(c_91870,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_14792,c_240]) ).

tcf(c_91871,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X1)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_373,c_240]) ).

tcf(c_91872,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),hAPP_real_real(plus_plus_real(X1),number267125858f_real(X2))) = hAPP_real_real(plus_plus_real(X1),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X2))),
    inference(superposition,[status(thm)],[c_389,c_240]) ).

tcf(c_91874,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),zero_zero_real)) = hAPP_real_real(plus_plus_real(X1),X0),
    inference(superposition,[status(thm)],[c_516,c_240]) ).

tcf(c_91886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2))),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_240,c_237]) ).

tcf(c_91887,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_real_real(plus_plus_real(X0),X2) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),X2)) != X1 ) ),
    inference(superposition,[status(thm)],[c_240,c_517]) ).

tcf(c_91890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3)) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X0),X3))),
    inference(superposition,[status(thm)],[c_240,c_237]) ).

tcf(c_91891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3))) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X0),X3))),
    inference(superposition,[status(thm)],[c_240,c_240]) ).

tcf(c_91892,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X2) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X2),X1)),
    inference(superposition,[status(thm)],[c_240,c_243]) ).

tcf(c_91893,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X1)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),
    inference(superposition,[status(thm)],[c_240,c_14792]) ).

tcf(c_91894,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_240,c_373]) ).

tcf(c_91895,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(plus_plus_real(X0),X1) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X1)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_240,c_521]) ).

tcf(c_91937,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),X1),
    inference(superposition,[status(thm)],[c_82861,c_252]) ).

tcf(c_91938,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)),
    inference(superposition,[status(thm)],[c_253,c_252]) ).

tcf(c_91941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_217,c_252]) ).

tcf(c_91943,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(pls),X1),
    inference(superposition,[status(thm)],[c_1004,c_252]) ).

tcf(c_91945,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(pls),X1)) = hAPP_int_int(times_times_int(pls),X1),
    inference(superposition,[status(thm)],[c_1001,c_252]) ).

tcf(c_91946,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(min),X0)) = hAPP_int_int(times_times_int(one_one_int),X0),
    inference(superposition,[status(thm)],[c_79464,c_252]) ).

tcf(c_91947,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(m),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),X1),
    inference(superposition,[status(thm)],[c_76855,c_252]) ).

tcf(c_91948,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(one_one_int),X0)) = hAPP_int_int(times_times_int(iPr_def_15),X0),
    inference(superposition,[status(thm)],[c_76925,c_252]) ).

tcf(c_91949,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(one_one_int),X0)) = hAPP_int_int(times_times_int(iPr_def_16),X0),
    inference(superposition,[status(thm)],[c_76926,c_252]) ).

tcf(c_91950,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(one_one_int),X0)) = hAPP_int_int(times_times_int(iPr_def_17),X0),
    inference(superposition,[status(thm)],[c_76927,c_252]) ).

tcf(c_91951,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(one_one_int),X0)) = hAPP_int_int(times_times_int(iPr_def_18),X0),
    inference(superposition,[status(thm)],[c_76928,c_252]) ).

tcf(c_91952,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_76995,c_252]) ).

tcf(c_91953,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(undefined_int(int)),X0)) = hAPP_int_int(times_times_int(undefined_int(int)),X0),
    inference(superposition,[status(thm)],[c_77063,c_252]) ).

tcf(c_91954,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),X1)) = hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),X1),
    inference(superposition,[status(thm)],[c_77069,c_252]) ).

tcf(c_91955,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),X1) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_79150,c_252]) ).

tcf(c_91956,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0),
    inference(superposition,[status(thm)],[c_88500,c_252]) ).

tcf(c_91957,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) = hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88519,c_252]) ).

tcf(c_91958,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) = hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88556,c_252]) ).

tcf(c_91959,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),X1) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_59637,c_252]) ).

tcf(c_91960,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X0)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_252,c_65]) ).

tcf(c_91961,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_int_int(times_times_int(X2),X2)))),
    inference(superposition,[status(thm)],[c_252,c_584]) ).

tcf(c_91962,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_82916]) ).

tcf(c_91963,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_83500]) ).

tcf(c_91964,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_82917]) ).

tcf(c_91965,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_83274]) ).

tcf(c_91966,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_82913]) ).

tcf(c_91967,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_82918]) ).

tcf(c_91968,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_252,c_82909]) ).

tcf(c_91969,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1))) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_252,c_82861]) ).

tcf(c_91970,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_252,c_11305]) ).

tcf(c_91971,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1))),hAPP_i1948725293t_bool(ord_less_eq_int,pls))),
    inference(superposition,[status(thm)],[c_252,c_76545]) ).

tcf(c_91972,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_252,c_1135]) ).

tcf(c_91974,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X0)))),
    inference(superposition,[status(thm)],[c_252,c_1042]) ).

tcf(c_91975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3)),
    inference(superposition,[status(thm)],[c_252,c_252]) ).

tcf(c_91976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X3),X2)),X2)),
    inference(superposition,[status(thm)],[c_252,c_833]) ).

tcf(c_91977,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_252,c_76863]) ).

tcf(c_91979,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_252,c_76535]) ).

tcf(c_91980,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)),hAPP_i1948725293t_bool(dvd_dvd_int,X2))),
    inference(superposition,[status(thm)],[c_252,c_76498]) ).

tcf(c_91981,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)))),
    inference(superposition,[status(thm)],[c_252,c_1045]) ).

tcf(c_91982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),X3)) = hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X3))),
    inference(superposition,[status(thm)],[c_252,c_217]) ).

tcf(c_91984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),X3)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X0),X3))),
    inference(superposition,[status(thm)],[c_252,c_217]) ).

tcf(c_91986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X3),X1))),X1)),
    inference(superposition,[status(thm)],[c_252,c_833]) ).

tcf(c_91987,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),pls)) = pls,
    inference(superposition,[status(thm)],[c_252,c_1001]) ).

tcf(c_91988,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),X2)))))),
    inference(superposition,[status(thm)],[c_252,c_584]) ).

tcf(c_91989,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),X2)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_83274]) ).

tcf(c_91990,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),X2)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_82919]) ).

tcf(c_91991,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),m)) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_252,c_76855]) ).

tcf(c_91992,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88556]) ).

tcf(c_91993,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88555]) ).

tcf(c_91994,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88553]) ).

tcf(c_91995,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88552]) ).

tcf(c_91996,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88558]) ).

tcf(c_91998,plain,
    ! [X0: $i,X1: $i] : legendre(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_84099]) ).

tcf(c_91999,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X0),X1))),
    inference(superposition,[status(thm)],[c_252,c_84098]) ).

tcf(c_92000,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),pls),hAPP_int_int(times_times_int(X0),X1))),
    inference(superposition,[status(thm)],[c_252,c_83491]) ).

tcf(c_92001,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(X0),X1),zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),pls))),
    inference(superposition,[status(thm)],[c_252,c_83489]) ).

tcf(c_92002,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_82983]) ).

tcf(c_92003,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_252,c_79557]) ).

tcf(c_92004,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_252,c_79437]) ).

tcf(c_92005,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_252,c_78410]) ).

tcf(c_92006,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_252,c_78402]) ).

tcf(c_92007,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_252,c_78328]) ).

tcf(c_92008,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_252,c_78307]) ).

tcf(c_92009,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)) != min,
    inference(superposition,[status(thm)],[c_252,c_80165]) ).

tcf(c_92010,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)) != iPr_def_15,
    inference(superposition,[status(thm)],[c_252,c_79551]) ).

tcf(c_92011,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)) != one_one_int,
    inference(superposition,[status(thm)],[c_252,c_79312]) ).

tcf(c_92012,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_252,c_79285]) ).

tcf(c_92013,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_252,c_79901]) ).

tcf(c_92014,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),
    inference(superposition,[status(thm)],[c_252,c_79239]) ).

tcf(c_92016,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_252,c_88550]) ).

tcf(c_92017,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_252,c_88551]) ).

tcf(c_92018,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X1)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_90959]) ).

tcf(c_92019,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_85345]) ).

tcf(c_92020,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_88495]) ).

tcf(c_92021,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2),sK30(iPr_def_19),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_88514]) ).

tcf(c_92022,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK14(hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_88551]) ).

tcf(c_92029,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),undefined_int(int))),
    inference(demodulation,[status(thm)],[c_80434,c_91937]) ).

tcf(c_92030,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),twoSqu1241645765sum2sq(X0))),
    inference(demodulation,[status(thm)],[c_80503,c_91937]) ).

tcf(c_92031,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_nat_int(X0,X1))),
    inference(demodulation,[status(thm)],[c_80436,c_91937]) ).

tcf(c_92032,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK26(iPr_def_14))),
    inference(demodulation,[status(thm)],[c_80433,c_91937]) ).

tcf(c_92033,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_83516,c_91937]) ).

tcf(c_92034,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_83515,c_91937]) ).

tcf(c_92035,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_83514,c_91937]) ).

tcf(c_92036,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(demodulation,[status(thm)],[c_83525,c_91937]) ).

tcf(c_92037,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(demodulation,[status(thm)],[c_84396,c_91937]) ).

tcf(c_92038,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(demodulation,[status(thm)],[c_81315,c_91937]) ).

tcf(c_92039,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(demodulation,[status(thm)],[c_85003,c_91937]) ).

tcf(c_92040,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_81465,c_91937]) ).

tcf(c_92041,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_81519,c_91937]) ).

tcf(c_92042,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_84321,c_91937]) ).

tcf(c_92043,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_12,m))),
    inference(demodulation,[status(thm)],[c_88204,c_91937]) ).

tcf(c_92044,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(min),m))),
    inference(demodulation,[status(thm)],[c_88167,c_91937]) ).

tcf(c_92045,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_89604,c_91937]) ).

tcf(c_92046,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(demodulation,[status(thm)],[c_88950,c_91937]) ).

tcf(c_92047,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X1),X0))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))),X0),
    inference(demodulation,[status(thm)],[c_78759,c_91955]) ).

tcf(c_92257,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(X0,X0,X2)),X1)) = sK14(X0,X0,X2) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_46106]) ).

tcf(c_92258,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK14(X0,X0,X2))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_46104]) ).

tcf(c_92259,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK14(X0,X0,X1)),pls) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_880]) ).

tcf(c_92260,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(sK14(X0,X0,X1)),one_one_nat) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_608]) ).

tcf(c_92261,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(X0,X0,X1)),pls) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_524]) ).

tcf(c_92262,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK14(X0,X0,X1)) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_523]) ).

tcf(c_92263,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK14(X0,X0,X1)) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_347]) ).

tcf(c_92264,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(X0,X0,X1)),one_one_int) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_346]) ).

tcf(c_92265,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(sK14(X0,X0,X1)) = sK14(X0,X0,X1) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88270,c_254]) ).

tcf(c_92366,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(X2,X0,one_one_int)),X1)) = sK14(X2,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_46106]) ).

tcf(c_92367,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK14(X2,X0,one_one_int))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_46104]) ).

tcf(c_92368,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK14(X1,X0,one_one_int)),pls) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_880]) ).

tcf(c_92369,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(sK14(X1,X0,one_one_int)),one_one_nat) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_608]) ).

tcf(c_92370,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(X1,X0,one_one_int)),pls) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_524]) ).

tcf(c_92371,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK14(X1,X0,one_one_int)) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_523]) ).

tcf(c_92372,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK14(X1,X0,one_one_int)) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_347]) ).

tcf(c_92373,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(X1,X0,one_one_int)),one_one_int) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_346]) ).

tcf(c_92374,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(sK14(X1,X0,one_one_int)) = sK14(X1,X0,one_one_int) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88271,c_254]) ).

tcf(c_92406,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(pls,X0,X0)),X1)) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_46106]) ).

tcf(c_92407,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK14(pls,X0,X0))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_46104]) ).

tcf(c_92408,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK14(pls,X0,X0)),pls) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_880]) ).

tcf(c_92409,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(sK14(pls,X0,X0)),one_one_nat) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_608]) ).

tcf(c_92410,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(pls,X0,X0)),pls) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_524]) ).

tcf(c_92411,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK14(pls,X0,X0)) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_523]) ).

tcf(c_92412,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK14(pls,X0,X0)) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_347]) ).

tcf(c_92413,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(pls,X0,X0)),one_one_int) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_346]) ).

tcf(c_92414,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(sK14(pls,X0,X0)) = sK14(pls,X0,X0) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88282,c_254]) ).

tcf(c_92437,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(pls,X0,min)),X1)) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_46106]) ).

tcf(c_92438,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK14(pls,X0,min))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_46104]) ).

tcf(c_92439,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK14(pls,X0,min)),pls) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_880]) ).

tcf(c_92440,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(sK14(pls,X0,min)),one_one_nat) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_608]) ).

tcf(c_92441,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(pls,X0,min)),pls) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_524]) ).

tcf(c_92442,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK14(pls,X0,min)) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_523]) ).

tcf(c_92443,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK14(pls,X0,min)) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_347]) ).

tcf(c_92444,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(pls,X0,min)),one_one_int) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_346]) ).

tcf(c_92445,plain,
    ! [X0: $i] :
      ( ( number_number_of_int(sK14(pls,X0,min)) = sK14(pls,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_88283,c_254]) ).

tcf(c_92467,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X0)) = pls,
    inference(superposition,[status(thm)],[c_82861,c_92002]) ).

tcf(c_92468,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),X1)),hAPP_int_int(times_times_int(X1),X0)) = pls,
    inference(superposition,[status(thm)],[c_253,c_92002]) ).

tcf(c_92470,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2)) = pls,
    inference(superposition,[status(thm)],[c_252,c_92002]) ).

tcf(c_92473,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(pls),hAPP_int_int(times_times_int(pls),X0)) = pls,
    inference(superposition,[status(thm)],[c_1004,c_92002]) ).

tcf(c_92475,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_92002]) ).

tcf(c_92478,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))) = pls,
    inference(superposition,[status(thm)],[c_252,c_92002]) ).

tcf(c_92479,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),pls)),hAPP_int_int(times_times_int(X0),pls)) = pls,
    inference(superposition,[status(thm)],[c_1004,c_92002]) ).

tcf(c_92480,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X0),one_one_int)) = pls,
    inference(superposition,[status(thm)],[c_76995,c_92002]) ).

tcf(c_92481,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X0),m)) = pls,
    inference(superposition,[status(thm)],[c_59637,c_92002]) ).

tcf(c_92482,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),hAPP_nat_int(power_power_int(X0),iPr_def_11)) = pls,
    inference(superposition,[status(thm)],[c_82861,c_92002]) ).

tcf(c_92483,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X1),X0)) = pls,
    inference(superposition,[status(thm)],[c_253,c_92002]) ).

tcf(c_92485,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))) = pls,
    inference(superposition,[status(thm)],[c_252,c_92002]) ).

tcf(c_92486,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2))) = pls,
    inference(superposition,[status(thm)],[c_217,c_92002]) ).

tcf(c_92488,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),pls) = pls,
    inference(superposition,[status(thm)],[c_1004,c_92002]) ).

tcf(c_92489,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = pls,
    inference(superposition,[status(thm)],[c_382,c_92002]) ).

tcf(c_92490,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))),pls) = pls,
    inference(superposition,[status(thm)],[c_1001,c_92002]) ).

tcf(c_92491,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_79464,c_92002]) ).

tcf(c_92492,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))),hAPP_int_int(iPr_def_13,X0)) = pls,
    inference(superposition,[status(thm)],[c_76855,c_92002]) ).

tcf(c_92493,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),iPr_def_15) = pls,
    inference(superposition,[status(thm)],[c_76925,c_92002]) ).

tcf(c_92494,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),iPr_def_16) = pls,
    inference(superposition,[status(thm)],[c_76926,c_92002]) ).

tcf(c_92495,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),iPr_def_17) = pls,
    inference(superposition,[status(thm)],[c_76927,c_92002]) ).

tcf(c_92496,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)))),iPr_def_18) = pls,
    inference(superposition,[status(thm)],[c_76928,c_92002]) ).

tcf(c_92497,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19)))),sK30(iPr_def_19)) = pls,
    inference(superposition,[status(thm)],[c_76995,c_92002]) ).

tcf(c_92498,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))),undefined_int(int)) = pls,
    inference(superposition,[status(thm)],[c_77063,c_92002]) ).

tcf(c_92499,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))),twoSqu1241645765sum2sq(X0)) = pls,
    inference(superposition,[status(thm)],[c_77069,c_92002]) ).

tcf(c_92500,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(X0),X0)) = pls,
    inference(superposition,[status(thm)],[c_79150,c_92002]) ).

tcf(c_92501,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_88500,c_92002]) ).

tcf(c_92502,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_88519,c_92002]) ).

tcf(c_92503,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = pls,
    inference(superposition,[status(thm)],[c_88556,c_92002]) ).

tcf(c_92504,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),hAPP_int_int(iPr_def_13,X0)) = pls,
    inference(superposition,[status(thm)],[c_59637,c_92002]) ).

tcf(c_92511,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),iPr_def_18) = pls,
    inference(light_normalisation,[status(thm)],[c_92496,c_76995]) ).

tcf(c_92512,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19))),iPr_def_17) = pls,
    inference(light_normalisation,[status(thm)],[c_92495,c_76995]) ).

tcf(c_92513,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),iPr_def_16) = pls,
    inference(light_normalisation,[status(thm)],[c_92494,c_76995]) ).

tcf(c_92514,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),iPr_def_15) = pls,
    inference(light_normalisation,[status(thm)],[c_92493,c_76995]) ).

tcf(c_92515,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),sK30(iPr_def_19)) = pls,
    inference(light_normalisation,[status(thm)],[c_92497,c_82489]) ).

tcf(c_92516,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))),hAPP_int_int(iPr_def_13,X0)) = pls,
    inference(light_normalisation,[status(thm)],[c_92492,c_59637]) ).

tcf(c_92518,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = pls,
    inference(light_normalisation,[status(thm)],[c_92489,c_79688,c_90934]) ).

tcf(c_92519,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),sK30(iPr_def_19))))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2))) = pls,
    inference(light_normalisation,[status(thm)],[c_92470,c_91938]) ).

tcf(c_92579,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X1),X2)),iPr_def_11)) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_90921,c_90904]) ).

tcf(c_92593,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X0),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),X1),
    inference(superposition,[status(thm)],[c_79150,c_255]) ).

tcf(c_92594,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
    inference(superposition,[status(thm)],[c_257,c_255]) ).

tcf(c_92596,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),X1),
    inference(superposition,[status(thm)],[c_76874,c_255]) ).

tcf(c_92598,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(pls),X0),
    inference(superposition,[status(thm)],[c_340,c_255]) ).

tcf(c_92600,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),t))),X0)) = hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),X0),
    inference(superposition,[status(thm)],[c_76316,c_255]) ).

tcf(c_92601,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),sK9))),X0)) = hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),X0),
    inference(superposition,[status(thm)],[c_76325,c_255]) ).

tcf(c_92602,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_76727,c_255]) ).

tcf(c_92603,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(undefined_int(int)),X0)) = hAPP_int_int(plus_plus_int(undefined_int(int)),X0),
    inference(superposition,[status(thm)],[c_77138,c_255]) ).

tcf(c_92604,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(min),X0)) = hAPP_int_int(plus_plus_int(min),X0),
    inference(superposition,[status(thm)],[c_77141,c_255]) ).

tcf(c_92605,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),X1)) = hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),X1),
    inference(superposition,[status(thm)],[c_77144,c_255]) ).

tcf(c_92606,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(m),X0)) = hAPP_int_int(plus_plus_int(m),X0),
    inference(superposition,[status(thm)],[c_77148,c_255]) ).

tcf(c_92607,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(s1),X0)) = hAPP_int_int(plus_plus_int(s1),X0),
    inference(superposition,[status(thm)],[c_77149,c_255]) ).

tcf(c_92608,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(s),X0)) = hAPP_int_int(plus_plus_int(s),X0),
    inference(superposition,[status(thm)],[c_77150,c_255]) ).

tcf(c_92609,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(t),X0)) = hAPP_int_int(plus_plus_int(t),X0),
    inference(superposition,[status(thm)],[c_77151,c_255]) ).

tcf(c_92610,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK9),X0)) = hAPP_int_int(plus_plus_int(sK9),X0),
    inference(superposition,[status(thm)],[c_77152,c_255]) ).

tcf(c_92611,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK10),X0)) = hAPP_int_int(plus_plus_int(sK10),X0),
    inference(superposition,[status(thm)],[c_77153,c_255]) ).

tcf(c_92612,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK11),X0)) = hAPP_int_int(plus_plus_int(sK11),X0),
    inference(superposition,[status(thm)],[c_77154,c_255]) ).

tcf(c_92613,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK13),X0)) = hAPP_int_int(plus_plus_int(sK13),X0),
    inference(superposition,[status(thm)],[c_77155,c_255]) ).

tcf(c_92614,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_77165,c_255]) ).

tcf(c_92615,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_15),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(iPr_def_15),X0),
    inference(superposition,[status(thm)],[c_77236,c_255]) ).

tcf(c_92616,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_16),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(iPr_def_16),X0),
    inference(superposition,[status(thm)],[c_77237,c_255]) ).

tcf(c_92617,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_17),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(iPr_def_17),X0),
    inference(superposition,[status(thm)],[c_77238,c_255]) ).

tcf(c_92618,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_18),hAPP_int_int(plus_plus_int(pls),X0)) = hAPP_int_int(plus_plus_int(iPr_def_18),X0),
    inference(superposition,[status(thm)],[c_77239,c_255]) ).

tcf(c_92619,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1),
    inference(superposition,[status(thm)],[c_78930,c_255]) ).

tcf(c_92620,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0),
    inference(superposition,[status(thm)],[c_78938,c_255]) ).

tcf(c_92621,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0),
    inference(superposition,[status(thm)],[c_79190,c_255]) ).

tcf(c_92622,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1),
    inference(superposition,[status(thm)],[c_79161,c_255]) ).

tcf(c_92623,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1),
    inference(superposition,[status(thm)],[c_79901,c_255]) ).

tcf(c_92624,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0),
    inference(superposition,[status(thm)],[c_79904,c_255]) ).

tcf(c_92625,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_83616,c_255]) ).

tcf(c_92626,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1),
    inference(superposition,[status(thm)],[c_85658,c_255]) ).

tcf(c_92627,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),X1)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88494,c_255]) ).

tcf(c_92628,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0),
    inference(superposition,[status(thm)],[c_88499,c_255]) ).

tcf(c_92629,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),X2)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X2),
    inference(superposition,[status(thm)],[c_88513,c_255]) ).

tcf(c_92630,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88518,c_255]) ).

tcf(c_92631,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),X2)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X2),
    inference(superposition,[status(thm)],[c_88550,c_255]) ).

tcf(c_92632,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) = hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88555,c_255]) ).

tcf(c_92633,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),X1) = hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_59636,c_255]) ).

tcf(c_92634,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X1) = pls )
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X1))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) != pls ) ),
    inference(superposition,[status(thm)],[c_255,c_519]) ).

tcf(c_92635,plain,
    ! [X0: $i,X1: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),
    inference(superposition,[status(thm)],[c_255,c_408]) ).

tcf(c_92636,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_255,c_79319]) ).

tcf(c_92637,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_255,c_79191]) ).

tcf(c_92638,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_255,c_79150]) ).

tcf(c_92639,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_255,c_78930]) ).

tcf(c_92640,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_255,c_78625]) ).

tcf(c_92641,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_255,c_78442]) ).

tcf(c_92642,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) != one_one_int,
    inference(superposition,[status(thm)],[c_255,c_77377]) ).

tcf(c_92643,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) != iPr_def_15,
    inference(superposition,[status(thm)],[c_255,c_76521]) ).

tcf(c_92644,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) != min,
    inference(superposition,[status(thm)],[c_255,c_755]) ).

tcf(c_92645,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X0)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_255,c_65]) ).

tcf(c_92646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2))),X3) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)),
    inference(superposition,[status(thm)],[c_255,c_255]) ).

tcf(c_92647,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)))
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_255,c_76880]) ).

tcf(c_92649,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))) != hAPP_int_int(plus_plus_int(X2),hAPP_int_int(iPr_def_12,X2)),
    inference(superposition,[status(thm)],[c_255,c_76515]) ).

tcf(c_92650,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X0)),
    inference(superposition,[status(thm)],[c_255,c_257]) ).

tcf(c_92651,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),one_one_int)) = hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_255,c_76874]) ).

tcf(c_92652,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1)))) != hAPP_int_int(plus_plus_int(X2),X2),
    inference(superposition,[status(thm)],[c_255,c_76515]) ).

tcf(c_92653,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1)))) != pls,
    inference(superposition,[status(thm)],[c_255,c_76368]) ).

tcf(c_92654,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_255,c_83504]) ).

tcf(c_92655,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_255,c_79957]) ).

tcf(c_92656,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X1)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_83616]) ).

tcf(c_92657,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_255,c_85658]) ).

tcf(c_92658,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(X0),X1)))) = sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_255,c_88494]) ).

tcf(c_92659,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(X0),X1)))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_255,c_88513]) ).

tcf(c_92660,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(X0),X1)))) = sK14(hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_255,c_88550]) ).

tcf(c_92665,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),X1) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X1)),
    inference(light_normalisation,[status(thm)],[c_92596,c_59636]) ).

tcf(c_92902,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X0)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(iPr_def_14),X0)),
    inference(superposition,[status(thm)],[c_79150,c_256]) ).

tcf(c_92905,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),one_one_int)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_76874,c_256]) ).

tcf(c_92906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X3))),
    inference(superposition,[status(thm)],[c_255,c_256]) ).

tcf(c_92909,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),pls),
    inference(superposition,[status(thm)],[c_340,c_256]) ).

tcf(c_92910,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(X1),number_number_of_int(X2))) = hAPP_int_int(plus_plus_int(X1),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X2))),
    inference(superposition,[status(thm)],[c_388,c_256]) ).

tcf(c_92911,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(t),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),t)))) = hAPP_int_int(plus_plus_int(X0),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_76316,c_256]) ).

tcf(c_92912,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),sK9)))) = hAPP_int_int(plus_plus_int(X0),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
    inference(superposition,[status(thm)],[c_76325,c_256]) ).

tcf(c_92913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),iPr_def_14),
    inference(superposition,[status(thm)],[c_76727,c_256]) ).

tcf(c_92914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),undefined_int(int))) = hAPP_int_int(plus_plus_int(X0),undefined_int(int)),
    inference(superposition,[status(thm)],[c_77138,c_256]) ).

tcf(c_92915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),min)) = hAPP_int_int(plus_plus_int(X0),min),
    inference(superposition,[status(thm)],[c_77141,c_256]) ).

tcf(c_92916,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),twoSqu1241645765sum2sq(X1))) = hAPP_int_int(plus_plus_int(X0),twoSqu1241645765sum2sq(X1)),
    inference(superposition,[status(thm)],[c_77144,c_256]) ).

tcf(c_92917,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),m)) = hAPP_int_int(plus_plus_int(X0),m),
    inference(superposition,[status(thm)],[c_77148,c_256]) ).

tcf(c_92918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),s1)) = hAPP_int_int(plus_plus_int(X0),s1),
    inference(superposition,[status(thm)],[c_77149,c_256]) ).

tcf(c_92919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),s)) = hAPP_int_int(plus_plus_int(X0),s),
    inference(superposition,[status(thm)],[c_77150,c_256]) ).

tcf(c_92920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),t)) = hAPP_int_int(plus_plus_int(X0),t),
    inference(superposition,[status(thm)],[c_77151,c_256]) ).

tcf(c_92921,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK9)) = hAPP_int_int(plus_plus_int(X0),sK9),
    inference(superposition,[status(thm)],[c_77152,c_256]) ).

tcf(c_92922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK10)) = hAPP_int_int(plus_plus_int(X0),sK10),
    inference(superposition,[status(thm)],[c_77153,c_256]) ).

tcf(c_92923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK11)) = hAPP_int_int(plus_plus_int(X0),sK11),
    inference(superposition,[status(thm)],[c_77154,c_256]) ).

tcf(c_92924,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK13)) = hAPP_int_int(plus_plus_int(X0),sK13),
    inference(superposition,[status(thm)],[c_77155,c_256]) ).

tcf(c_92925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_77165,c_256]) ).

tcf(c_92926,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_15),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),iPr_def_15),
    inference(superposition,[status(thm)],[c_77236,c_256]) ).

tcf(c_92927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_16),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),iPr_def_16),
    inference(superposition,[status(thm)],[c_77237,c_256]) ).

tcf(c_92928,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_17),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),iPr_def_17),
    inference(superposition,[status(thm)],[c_77238,c_256]) ).

tcf(c_92929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(iPr_def_18),hAPP_int_int(plus_plus_int(X0),pls)) = hAPP_int_int(plus_plus_int(X0),iPr_def_18),
    inference(superposition,[status(thm)],[c_77239,c_256]) ).

tcf(c_92930,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),X1)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_78930,c_256]) ).

tcf(c_92931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_15)),
    inference(superposition,[status(thm)],[c_78938,c_256]) ).

tcf(c_92932,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),m)) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(superposition,[status(thm)],[c_79190,c_256]) ).

tcf(c_92933,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X1)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),
    inference(superposition,[status(thm)],[c_79161,c_256]) ).

tcf(c_92934,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X1),iPr_def_14)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79901,c_256]) ).

tcf(c_92935,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79904,c_256]) ).

tcf(c_92936,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_83616,c_256]) ).

tcf(c_92937,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_85658,c_256]) ).

tcf(c_92938,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))) = hAPP_int_int(plus_plus_int(X1),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88494,c_256]) ).

tcf(c_92939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88499,c_256]) ).

tcf(c_92940,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2),sK30(iPr_def_19),sK30(iPr_def_19))),X0))) = hAPP_int_int(plus_plus_int(X1),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X2),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88513,c_256]) ).

tcf(c_92941,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88518,c_256]) ).

tcf(c_92942,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))) = hAPP_int_int(plus_plus_int(X1),sK14(hAPP_int_int(times_times_int(X2),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88550,c_256]) ).

tcf(c_92943,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88555,c_256]) ).

tcf(c_92944,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X1)) = hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_59636,c_256]) ).

tcf(c_92967,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X1) = pls )
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X1))
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) != pls ) ),
    inference(superposition,[status(thm)],[c_256,c_519]) ).

tcf(c_92968,plain,
    ! [X0: $i,X1: $i] : number267125858f_real(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X1))),
    inference(superposition,[status(thm)],[c_256,c_408]) ).

tcf(c_92969,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X1))))),
    inference(superposition,[status(thm)],[c_256,c_79319]) ).

tcf(c_92970,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))),
    inference(superposition,[status(thm)],[c_256,c_79191]) ).

tcf(c_92971,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_256,c_79150]) ).

tcf(c_92972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_256,c_78930]) ).

tcf(c_92973,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) = hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))),
    inference(superposition,[status(thm)],[c_256,c_78625]) ).

tcf(c_92974,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))),
    inference(superposition,[status(thm)],[c_256,c_78442]) ).

tcf(c_92975,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) != one_one_int,
    inference(superposition,[status(thm)],[c_256,c_77377]) ).

tcf(c_92976,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) != iPr_def_15,
    inference(superposition,[status(thm)],[c_256,c_76521]) ).

tcf(c_92977,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) != min,
    inference(superposition,[status(thm)],[c_256,c_755]) ).

tcf(c_92978,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X2),X1)))
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_256,c_65]) ).

tcf(c_92979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2))),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_256,c_255]) ).

tcf(c_92980,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_256,c_76880]) ).

tcf(c_92982,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)) != hAPP_int_int(plus_plus_int(X2),hAPP_int_int(iPr_def_12,X2)),
    inference(superposition,[status(thm)],[c_256,c_76515]) ).

tcf(c_92983,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X2),X1)),
    inference(superposition,[status(thm)],[c_256,c_257]) ).

tcf(c_92984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X0),X3))),
    inference(superposition,[status(thm)],[c_256,c_256]) ).

tcf(c_92986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X0),X3))),
    inference(superposition,[status(thm)],[c_256,c_255]) ).

tcf(c_92987,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_256,c_79918]) ).

tcf(c_92988,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_256,c_79931]) ).

tcf(c_92993,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X1)) = hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X0)),
    inference(light_normalisation,[status(thm)],[c_92905,c_92651]) ).

tcf(c_92997,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)) != hAPP_int_int(plus_plus_int(X1),X1),
    inference(demodulation,[status(thm)],[c_76515,c_92944]) ).

tcf(c_92998,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)) != pls,
    inference(demodulation,[status(thm)],[c_76368,c_92944]) ).

tcf(c_93204,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_79150,c_276]) ).

tcf(c_93206,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_255,c_276]) ).

tcf(c_93207,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_256,c_276]) ).

tcf(c_93210,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_388,c_276]) ).

tcf(c_93211,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),m)) ),
    inference(superposition,[status(thm)],[c_79190,c_276]) ).

tcf(c_93212,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59636,c_276]) ).

tcf(c_93213,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_276,c_226]) ).

tcf(c_93214,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_93212,c_59638]) ).

tcf(c_93221,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
    inference(light_normalisation,[status(thm)],[c_93210,c_79988]) ).

tcf(c_93224,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(light_normalisation,[status(thm)],[c_93207,c_92971]) ).

tcf(c_93239,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(superposition,[status(thm)],[c_79150,c_277]) ).

tcf(c_93241,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) ),
    inference(superposition,[status(thm)],[c_255,c_277]) ).

tcf(c_93242,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) ),
    inference(superposition,[status(thm)],[c_256,c_277]) ).

tcf(c_93245,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(superposition,[status(thm)],[c_388,c_277]) ).

tcf(c_93246,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_13,iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_79190,c_277]) ).

tcf(c_93252,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(light_normalisation,[status(thm)],[c_93245,c_79988]) ).

tcf(c_93255,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1)))) ),
    inference(light_normalisation,[status(thm)],[c_93242,c_92971]) ).

tcf(c_93286,plain,
    hBOOL(member_int(m,zcong(pls,pls))),
    inference(superposition,[status(thm)],[c_76363,c_90016]) ).

tcf(c_93287,plain,
    hBOOL(member_int(m,zcong(m,pls))),
    inference(superposition,[status(thm)],[c_76934,c_90016]) ).

tcf(c_93293,plain,
    hBOOL(hAPP_int_bool(zcong(pls,m),m)),
    inference(superposition,[status(thm)],[c_76934,c_90018]) ).

tcf(c_93296,plain,
    ! [X0: $i] : hBOOL(member_int(m,zcong(pls,hAPP_int_int(iPr_def_13,X0)))),
    inference(superposition,[status(thm)],[c_90018,c_226]) ).

tcf(c_93297,plain,
    ! [X0: $i] :
      ( is_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m))
      | ~ is_int(hAPP_int_int(iPr_def_13,X0)) ),
    inference(superposition,[status(thm)],[c_90018,c_852]) ).

tcf(c_93299,plain,
    ! [X0: $i] : is_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)),
    inference(forward_subsumption_resolution,[status(thm)],[c_93297,c_77054]) ).

tcf(c_93304,plain,
    is_int(sK14(pls,m,m)),
    inference(superposition,[status(thm)],[c_76934,c_93299]) ).

tcf(c_93307,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,hAPP_int_int(iPr_def_13,X1),m)),X0)) = sK14(pls,hAPP_int_int(iPr_def_13,X1),m),
    inference(superposition,[status(thm)],[c_93299,c_46106]) ).

tcf(c_93308,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,hAPP_int_int(iPr_def_13,X1),m))),X0) = pls,
    inference(superposition,[status(thm)],[c_93299,c_46104]) ).

tcf(c_93309,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)),pls) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_880]) ).

tcf(c_93310,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)),one_one_nat) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_608]) ).

tcf(c_93311,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)),pls) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_524]) ).

tcf(c_93312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK14(pls,hAPP_int_int(iPr_def_13,X0),m)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_523]) ).

tcf(c_93313,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(pls,hAPP_int_int(iPr_def_13,X0),m)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_347]) ).

tcf(c_93314,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)),one_one_int) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_346]) ).

tcf(c_93315,plain,
    ! [X0: $i] : number_number_of_int(sK14(pls,hAPP_int_int(iPr_def_13,X0),m)) = sK14(pls,hAPP_int_int(iPr_def_13,X0),m),
    inference(superposition,[status(thm)],[c_93299,c_254]) ).

tcf(c_93329,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_79150,c_92614]) ).

tcf(c_93332,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_12,sK30(iPr_def_19))) = hAPP_int_int(iPr_def_12,sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_76874,c_92614]) ).

tcf(c_93341,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1),
    inference(superposition,[status(thm)],[c_92614,c_255]) ).

tcf(c_93342,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_92614,c_76880]) ).

tcf(c_93343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),
    inference(superposition,[status(thm)],[c_92614,c_256]) ).

tcf(c_93345,plain,
    ! [X0: $i] : is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_93342,c_57]) ).

tcf(c_93367,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_92925,c_255]) ).

tcf(c_93368,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))
      | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_92925,c_76880]) ).

tcf(c_93369,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_92925,c_256]) ).

tcf(c_93371,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(pls),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92925,c_256]) ).

tcf(c_93373,plain,
    ! [X0: $i] : is_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(forward_subsumption_resolution,[status(thm)],[c_93368,c_57]) ).

tcf(c_93384,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_59636,c_92625]) ).

tcf(c_93385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_79150,c_92625]) ).

tcf(c_93386,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_257,c_92625]) ).

tcf(c_93388,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),one_one_int),
    inference(superposition,[status(thm)],[c_76874,c_92625]) ).

tcf(c_93389,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X2))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),X2)),
    inference(superposition,[status(thm)],[c_256,c_92625]) ).

tcf(c_93391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_83616,c_92625]) ).

tcf(c_93392,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_85658,c_92625]) ).

tcf(c_93393,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88494,c_92625]) ).

tcf(c_93394,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))) = hAPP_int_int(plus_plus_int(X1),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88513,c_92625]) ).

tcf(c_93395,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))) = hAPP_int_int(plus_plus_int(X1),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88550,c_92625]) ).

tcf(c_93398,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_92625,c_65]) ).

tcf(c_93399,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X2),
    inference(superposition,[status(thm)],[c_92625,c_255]) ).

tcf(c_93400,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_92625,c_76880]) ).

tcf(c_93401,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X2))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X2)),
    inference(superposition,[status(thm)],[c_92625,c_256]) ).

tcf(c_93403,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X1))),X2))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X2),
    inference(superposition,[status(thm)],[c_92625,c_255]) ).

tcf(c_93404,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_92625,c_79918]) ).

tcf(c_93406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))),X0))) = number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_92625,c_79931]) ).

tcf(c_93407,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),X1)) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),
    inference(superposition,[status(thm)],[c_92625,c_92625]) ).

tcf(c_93408,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),pls)),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92625,c_92925]) ).

tcf(c_93414,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0))) = hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_93404,c_80219]) ).

tcf(c_93415,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))),X0))) = hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_93406,c_80219]) ).

tcf(c_93482,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_92656]) ).

tcf(c_93483,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),one_one_int)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_92656]) ).

tcf(c_93484,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(iPr_def_14),X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79150,c_92656]) ).

tcf(c_93487,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_92656]) ).

tcf(c_93488,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_92656]) ).

tcf(c_93489,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_92656]) ).

tcf(c_93491,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),pls))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_340,c_92656]) ).

tcf(c_93492,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_388,c_92656]) ).

tcf(c_93493,plain,
    hAPP_int_int(plus_plus_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),t))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76316,c_92656]) ).

tcf(c_93494,plain,
    hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_16),sK9))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76325,c_92656]) ).

tcf(c_93495,plain,
    hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_14))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76727,c_92656]) ).

tcf(c_93496,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(undefined_int(int)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),undefined_int(int)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77138,c_92656]) ).

tcf(c_93497,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(min),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),min))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77141,c_92656]) ).

tcf(c_93498,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77144,c_92656]) ).

tcf(c_93499,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77148,c_92656]) ).

tcf(c_93500,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(s1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),s1))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77149,c_92656]) ).

tcf(c_93501,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(s),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),s))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77150,c_92656]) ).

tcf(c_93502,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(t),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),t))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77151,c_92656]) ).

tcf(c_93503,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK9),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK9))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77152,c_92656]) ).

tcf(c_93504,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK10),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK10))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77153,c_92656]) ).

tcf(c_93505,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK11),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK11))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77154,c_92656]) ).

tcf(c_93506,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK13),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK13))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77155,c_92656]) ).

tcf(c_93507,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77165,c_92656]) ).

tcf(c_93508,plain,
    hAPP_int_int(plus_plus_int(iPr_def_15),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_15))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77236,c_92656]) ).

tcf(c_93509,plain,
    hAPP_int_int(plus_plus_int(iPr_def_16),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_16))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77237,c_92656]) ).

tcf(c_93510,plain,
    hAPP_int_int(plus_plus_int(iPr_def_17),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_17))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77238,c_92656]) ).

tcf(c_93511,plain,
    hAPP_int_int(plus_plus_int(iPr_def_18),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),iPr_def_18))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_77239,c_92656]) ).

tcf(c_93512,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_92656]) ).

tcf(c_93513,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_92656]) ).

tcf(c_93514,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_92656]) ).

tcf(c_93515,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_92656]) ).

tcf(c_93516,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_92656]) ).

tcf(c_93517,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_92656]) ).

tcf(c_93518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_92656]) ).

tcf(c_93519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_92656]) ).

tcf(c_93520,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_92656]) ).

tcf(c_93521,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88499,c_92656]) ).

tcf(c_93522,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_92656]) ).

tcf(c_93523,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88518,c_92656]) ).

tcf(c_93524,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_92656]) ).

tcf(c_93525,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88555,c_92656]) ).

tcf(c_93527,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92614,c_92656]) ).

tcf(c_93528,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_92656]) ).

tcf(c_93529,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92925,c_92656]) ).

tcf(c_93530,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_92656]) ).

tcf(c_93532,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X1)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_92656]) ).

tcf(c_93533,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X1)))),X2)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X2),
    inference(superposition,[status(thm)],[c_92656,c_255]) ).

tcf(c_93535,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X2))))) = hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92656,c_256]) ).

tcf(c_93537,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_255]) ).

tcf(c_93538,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_256]) ).

tcf(c_93540,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92656,c_79918]) ).

tcf(c_93542,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92656,c_79931]) ).

tcf(c_93543,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)),X0)))) = hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92656,c_92625]) ).

tcf(c_93544,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(pls),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_92614]) ).

tcf(c_93545,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_92625]) ).

tcf(c_93547,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93544,c_77165]) ).

tcf(c_93548,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93487,c_59636]) ).

tcf(c_93551,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93540,c_76415]) ).

tcf(c_93552,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93542,c_76415]) ).

tcf(c_93553,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X2),X1)))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93537,c_92983]) ).

tcf(c_93728,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_59636,c_92936]) ).

tcf(c_93729,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_79150,c_92936]) ).

tcf(c_93730,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),X1)) = hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_257,c_92936]) ).

tcf(c_93732,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_255,c_92936]) ).

tcf(c_93733,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(iPr_def_12,sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_59636,c_92936]) ).

tcf(c_93736,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_92656]) ).

tcf(c_93737,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X2),
    inference(superposition,[status(thm)],[c_92936,c_255]) ).

tcf(c_93738,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_92936,c_76880]) ).

tcf(c_93739,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_92936,c_256]) ).

tcf(c_93741,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),X1))))) = hAPP_int_int(plus_plus_int(X2),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92936,c_255]) ).

tcf(c_93742,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92936,c_256]) ).

tcf(c_93744,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_92936,c_79918]) ).

tcf(c_93746,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_92936,c_79931]) ).

tcf(c_93747,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_92936,c_92625]) ).

tcf(c_93748,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),pls)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_92936,c_92614]) ).

tcf(c_93749,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),
    inference(superposition,[status(thm)],[c_92936,c_92625]) ).

tcf(c_93753,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_93744,c_80178]) ).

tcf(c_93754,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_93746,c_80178]) ).

tcf(c_93788,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_93551]) ).

tcf(c_93789,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79931,c_93551]) ).

tcf(c_93790,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_93551]) ).

tcf(c_93791,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_93551]) ).

tcf(c_93792,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_93551]) ).

tcf(c_93794,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_93551]) ).

tcf(c_93795,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_93551]) ).

tcf(c_93797,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_93551]) ).

tcf(c_93798,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_93551]) ).

tcf(c_93799,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_93551]) ).

tcf(c_93800,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_93551]) ).

tcf(c_93801,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_93551]) ).

tcf(c_93802,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_93551]) ).

tcf(c_93803,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_93551]) ).

tcf(c_93804,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_93551]) ).

tcf(c_93805,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_93551]) ).

tcf(c_93806,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_93551]) ).

tcf(c_93807,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_93551]) ).

tcf(c_93808,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_93551]) ).

tcf(c_93809,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_93551]) ).

tcf(c_93810,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_93551]) ).

tcf(c_93813,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_92656]) ).

tcf(c_93814,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_93551,c_255]) ).

tcf(c_93816,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_256]) ).

tcf(c_93818,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_93551]) ).

tcf(c_93819,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_79918]) ).

tcf(c_93820,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93794,c_59636]) ).

tcf(c_93821,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93788,c_79190]) ).

tcf(c_93822,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93819,c_76415]) ).

tcf(c_93867,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(pls),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_77431,c_93391]) ).

tcf(c_93869,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93391,c_92656]) ).

tcf(c_93870,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_93391,c_255]) ).

tcf(c_93872,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93391,c_256]) ).

tcf(c_93875,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93391,c_79931]) ).

tcf(c_93876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93391,c_92936]) ).

tcf(c_93878,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(light_normalisation,[status(thm)],[c_93875,c_80178]) ).

tcf(c_93879,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),
    inference(light_normalisation,[status(thm)],[c_93870,c_93407]) ).

tcf(c_93890,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),X0),
    inference(demodulation,[status(thm)],[c_368,c_76874]) ).

tcf(c_93892,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),one_one_int) = hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),one_one_int)),
    inference(superposition,[status(thm)],[c_59636,c_93890]) ).

tcf(c_93893,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_nat_int(power_power_int(X0),iPr_def_11)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),X0),
    inference(superposition,[status(thm)],[c_82861,c_93890]) ).

tcf(c_93894,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X0),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),X0),
    inference(superposition,[status(thm)],[c_253,c_93890]) ).

tcf(c_93896,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X0))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),X2))),X0),
    inference(superposition,[status(thm)],[c_252,c_93890]) ).

tcf(c_93897,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X2),X1))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X2)),hAPP_int_int(times_times_int(X0),X1)),
    inference(superposition,[status(thm)],[c_217,c_93890]) ).

tcf(c_93899,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,pls)),X0) = hAPP_int_int(plus_plus_int(X0),pls),
    inference(superposition,[status(thm)],[c_1004,c_93890]) ).

tcf(c_93900,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(X1),X0))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,number_number_of_int(X1))),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_382,c_93890]) ).

tcf(c_93901,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),pls) = hAPP_int_int(plus_plus_int(pls),pls),
    inference(superposition,[status(thm)],[c_1001,c_93890]) ).

tcf(c_93902,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,min)),min) = hAPP_int_int(plus_plus_int(min),one_one_int),
    inference(superposition,[status(thm)],[c_79464,c_93890]) ).

tcf(c_93903,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m) = hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)),
    inference(superposition,[status(thm)],[c_76855,c_93890]) ).

tcf(c_93904,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_15)),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),iPr_def_15),
    inference(superposition,[status(thm)],[c_76925,c_93890]) ).

tcf(c_93905,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_16)),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),iPr_def_16),
    inference(superposition,[status(thm)],[c_76926,c_93890]) ).

tcf(c_93906,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_17)),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),iPr_def_17),
    inference(superposition,[status(thm)],[c_76927,c_93890]) ).

tcf(c_93907,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_18)),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),iPr_def_18),
    inference(superposition,[status(thm)],[c_76928,c_93890]) ).

tcf(c_93908,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_76995,c_93890]) ).

tcf(c_93909,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),undefined_int(int)) = hAPP_int_int(plus_plus_int(undefined_int(int)),undefined_int(int)),
    inference(superposition,[status(thm)],[c_77063,c_93890]) ).

tcf(c_93910,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),twoSqu1241645765sum2sq(X0)) = hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),twoSqu1241645765sum2sq(X0)),
    inference(superposition,[status(thm)],[c_77069,c_93890]) ).

tcf(c_93911,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_14)),X0),
    inference(superposition,[status(thm)],[c_79150,c_93890]) ).

tcf(c_93912,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88500,c_93890]) ).

tcf(c_93913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88519,c_93890]) ).

tcf(c_93914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_88556,c_93890]) ).

tcf(c_93915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,X0)) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0),
    inference(superposition,[status(thm)],[c_59637,c_93890]) ).

tcf(c_93916,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),X1))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_93890,c_65]) ).

tcf(c_93917,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),X0)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_92656]) ).

tcf(c_93918,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X0)),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),X0)),X2),
    inference(superposition,[status(thm)],[c_93890,c_255]) ).

tcf(c_93919,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),X0))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_93890,c_76880]) ).

tcf(c_93920,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X2),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X2)),X0)),
    inference(superposition,[status(thm)],[c_93890,c_256]) ).

tcf(c_93922,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X2)),hAPP_int_int(plus_plus_int(X0),X1)),
    inference(superposition,[status(thm)],[c_93890,c_255]) ).

tcf(c_93923,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_93890,c_584]) ).

tcf(c_93924,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_83274]) ).

tcf(c_93925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_93551]) ).

tcf(c_93926,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(X0),m))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),
    inference(superposition,[status(thm)],[c_93890,c_79918]) ).

tcf(c_93927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93890,c_92614]) ).

tcf(c_93928,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93890,c_79931]) ).

tcf(c_93929,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93890,c_92625]) ).

tcf(c_93930,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),iPr_def_11))),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_82919]) ).

tcf(c_93931,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,m))),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_83500]) ).

tcf(c_93934,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_18)),one_one_int) = hAPP_int_int(iPr_def_12,iPr_def_18),
    inference(light_normalisation,[status(thm)],[c_93907,c_59636]) ).

tcf(c_93936,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,iPr_def_16)),one_one_int) = hAPP_int_int(iPr_def_12,iPr_def_16),
    inference(light_normalisation,[status(thm)],[c_93905,c_59636]) ).

tcf(c_93938,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),pls) = pls,
    inference(light_normalisation,[status(thm)],[c_93901,c_340]) ).

tcf(c_93942,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),one_one_int)) = hAPP_int_int(iPr_def_12,X0),
    inference(light_normalisation,[status(thm)],[c_93892,c_78023]) ).

tcf(c_93943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X0),X0)) = hAPP_int_int(times_times_int(iPr_def_15),X0),
    inference(light_normalisation,[status(thm)],[c_93911,c_59639]) ).

tcf(c_93944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),twoSqu1241645765sum2sq(X0)) = hAPP_int_int(times_times_int(iPr_def_14),twoSqu1241645765sum2sq(X0)),
    inference(light_normalisation,[status(thm)],[c_93910,c_59638]) ).

tcf(c_93945,plain,
    hAPP_int_int(plus_plus_int(undefined_int(int)),undefined_int(int)) = hAPP_int_int(times_times_int(iPr_def_14),undefined_int(int)),
    inference(light_normalisation,[status(thm)],[c_93909,c_59638]) ).

tcf(c_93946,plain,
    hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_93908,c_59638]) ).

tcf(c_93947,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)) = hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_93926,c_76855,c_77366]) ).

tcf(c_93948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_93928,c_79557]) ).

tcf(c_93949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_93925,c_76855]) ).

tcf(c_93950,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_14),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_93912,c_59638]) ).

tcf(c_93951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_14),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_93914,c_59638]) ).

tcf(c_93952,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_14),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_93913,c_59638]) ).

tcf(c_94015,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X0)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X0),
    inference(demodulation,[status(thm)],[c_369,c_77521]) ).

tcf(c_94017,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),one_one_nat) = hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(times_times_nat(X0),one_one_nat)),
    inference(superposition,[status(thm)],[c_59634,c_94015]) ).

tcf(c_94018,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(power_power_nat(X0),iPr_def_11)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X0),
    inference(superposition,[status(thm)],[c_82316,c_94015]) ).

tcf(c_94020,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X2),X1))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),hAPP_nat_nat(times_times_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_218,c_94015]) ).

tcf(c_94022,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X0),
    inference(superposition,[status(thm)],[c_1309,c_94015]) ).

tcf(c_94023,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),one_one_nat) = hAPP_nat_nat(plus_plus_nat(one_one_nat),X0),
    inference(superposition,[status(thm)],[c_1413,c_94015]) ).

tcf(c_94024,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,one_one_nat)),X0) = hAPP_nat_nat(plus_plus_nat(X0),X0),
    inference(superposition,[status(thm)],[c_1417,c_94015]) ).

tcf(c_94025,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,zero_zero_nat)),X0) = hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1336,c_94015]) ).

tcf(c_94026,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1337,c_94015]) ).

tcf(c_94029,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_94015,c_1324]) ).

tcf(c_94030,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_94015,c_1323]) ).

tcf(c_94031,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1) != X1 ) ),
    inference(superposition,[status(thm)],[c_94015,c_1321]) ).

tcf(c_94033,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),hAPP_nat_nat(times_times_nat(X0),X1))),
    inference(superposition,[status(thm)],[c_94015,c_1344]) ).

tcf(c_94034,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),X1)),
    inference(superposition,[status(thm)],[c_94015,c_1343]) ).

tcf(c_94035,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_94015,c_1327]) ).

tcf(c_94036,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),X1) = hAPP_nat_nat(times_times_nat(X0),X1),
    inference(superposition,[status(thm)],[c_94015,c_1290]) ).

tcf(c_94037,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),hAPP_nat_nat(times_times_nat(X0),X1)) = X1,
    inference(superposition,[status(thm)],[c_94015,c_1289]) ).

tcf(c_94039,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X0))),
    inference(superposition,[status(thm)],[c_94015,c_1375]) ).

tcf(c_94040,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = X2 )
      | ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1) != hAPP_nat_nat(plus_plus_nat(X1),X2) ) ),
    inference(superposition,[status(thm)],[c_94015,c_1287]) ).

tcf(c_94041,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1))),
    inference(superposition,[status(thm)],[c_94015,c_1373]) ).

tcf(c_94042,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),zero_zero_nat) = hAPP_nat_nat(times_times_nat(X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_94015,c_1326]) ).

tcf(c_94043,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X2) ) ),
    inference(superposition,[status(thm)],[c_94015,c_1288]) ).

tcf(c_94044,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),zero_zero_nat) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_94042,c_1337]) ).

tcf(c_94047,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),one_one_nat) = hAPP_nat_nat(iPr_def_10,X0),
    inference(light_normalisation,[status(thm)],[c_94023,c_59634]) ).

tcf(c_94161,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),one_one_real)),X0) = hAPP_real_real(plus_plus_real(X0),hAPP_nat_real(power_power_real(X0),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82839,c_370]) ).

tcf(c_94163,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X2),X1))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X2),one_one_real)),hAPP_real_real(times_times_real(X0),X1)),
    inference(superposition,[status(thm)],[c_219,c_370]) ).

tcf(c_94165,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),X0),
    inference(superposition,[status(thm)],[c_976,c_370]) ).

tcf(c_94168,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),one_one_real)),X0) = hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X0),X0)),
    inference(superposition,[status(thm)],[c_373,c_370]) ).

tcf(c_94169,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(hAPP_int_int(times_times_int(X1),X0))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real)),number267125858f_real(X0)),
    inference(superposition,[status(thm)],[c_383,c_370]) ).

tcf(c_94170,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),one_one_real)),number267125858f_real(X0)) = hAPP_real_real(plus_plus_real(number267125858f_real(X0)),number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_408,c_370]) ).

tcf(c_94171,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(zero_zero_real),one_one_real)),X0) = hAPP_real_real(plus_plus_real(X0),zero_zero_real),
    inference(superposition,[status(thm)],[c_1002,c_370]) ).

tcf(c_94172,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(plus_plus_real(X0),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),one_one_real)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),
    inference(superposition,[status(thm)],[c_14792,c_370]) ).

tcf(c_94179,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),X2)),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),one_one_real))),X0),
    inference(superposition,[status(thm)],[c_237,c_370]) ).

tcf(c_94180,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),X1)),X0),
    inference(superposition,[status(thm)],[c_243,c_370]) ).

tcf(c_94181,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(zero_zero_real),X0)) = hAPP_real_real(times_times_real(one_one_real),X0),
    inference(superposition,[status(thm)],[c_508,c_370]) ).

tcf(c_94182,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X0)),X2)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),X0)),X2),
    inference(superposition,[status(thm)],[c_370,c_237]) ).

tcf(c_94183,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real )
      | ( hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),one_one_real)),X1) != X1 ) ),
    inference(superposition,[status(thm)],[c_370,c_517]) ).

tcf(c_94185,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(X2),hAPP_real_real(plus_plus_real(X0),X1)))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X2),one_one_real)),hAPP_real_real(plus_plus_real(X0),X1)),
    inference(superposition,[status(thm)],[c_370,c_237]) ).

tcf(c_94186,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(X2),X0))) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X2),one_one_real)),X0)),
    inference(superposition,[status(thm)],[c_370,c_240]) ).

tcf(c_94187,plain,
    ! [X0: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),one_one_real)),hAPP_real_real(times_times_real(X0),X0)))),
    inference(superposition,[status(thm)],[c_370,c_585]) ).

tcf(c_94189,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X0),one_one_real)),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(X0),X1)))),
    inference(superposition,[status(thm)],[c_370,c_1043]) ).

tcf(c_94190,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(X2),X1))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X2),one_one_real)),hAPP_real_real(times_times_real(X0),X1)),
    inference(superposition,[status(thm)],[c_370,c_219]) ).

tcf(c_94192,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),one_one_real)),X0),
    inference(superposition,[status(thm)],[c_370,c_370]) ).

tcf(c_94193,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) = hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),one_one_real)),
    inference(superposition,[status(thm)],[c_370,c_976]) ).

tcf(c_94194,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)))),
    inference(superposition,[status(thm)],[c_370,c_1040]) ).

tcf(c_94195,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(one_one_real),hAPP_real_real(times_times_real(X0),one_one_real)) = hAPP_real_real(plus_plus_real(X0),one_one_real),
    inference(superposition,[status(thm)],[c_370,c_325]) ).

tcf(c_94196,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(one_one_real),X0)) = hAPP_real_real(plus_plus_real(X0),X0),
    inference(superposition,[status(thm)],[c_370,c_373]) ).

tcf(c_94197,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(zero_zero_real),hAPP_real_real(times_times_real(X0),zero_zero_real)) = zero_zero_real,
    inference(superposition,[status(thm)],[c_370,c_999]) ).

tcf(c_94200,plain,
    ! [X0: $i] : hAPP_real_real(plus_plus_real(X0),one_one_real) = hAPP_real_real(plus_plus_real(one_one_real),X0),
    inference(light_normalisation,[status(thm)],[c_94195,c_325]) ).

tcf(c_94202,plain,
    ! [X0: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(zero_zero_real),one_one_real)),X0) = X0,
    inference(light_normalisation,[status(thm)],[c_94171,c_516]) ).

tcf(c_94334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(pls,m,m)),X0)) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_46106]) ).

tcf(c_94335,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(pls,m,m))),X0) = pls,
    inference(superposition,[status(thm)],[c_93304,c_46104]) ).

tcf(c_94336,plain,
    hAPP_int_int(minus_minus_int(sK14(pls,m,m)),pls) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_880]) ).

tcf(c_94337,plain,
    hAPP_nat_int(power_power_int(sK14(pls,m,m)),one_one_nat) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_608]) ).

tcf(c_94338,plain,
    hAPP_int_int(plus_plus_int(sK14(pls,m,m)),pls) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_524]) ).

tcf(c_94339,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(pls,m,m)) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_523]) ).

tcf(c_94340,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(pls,m,m)) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_347]) ).

tcf(c_94341,plain,
    hAPP_int_int(times_times_int(sK14(pls,m,m)),one_one_int) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_346]) ).

tcf(c_94342,plain,
    number_number_of_int(sK14(pls,m,m)) = sK14(pls,m,m),
    inference(superposition,[status(thm)],[c_93304,c_254]) ).

tcf(c_94374,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79150,c_93345]) ).

tcf(c_94377,plain,
    is_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76874,c_93345]) ).

tcf(c_94378,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_256,c_93345]) ).

tcf(c_94380,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93890,c_93345]) ).

tcf(c_94390,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_93345,c_46106]) ).

tcf(c_94391,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),X0) = pls,
    inference(superposition,[status(thm)],[c_93345,c_46104]) ).

tcf(c_94392,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),pls) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_880]) ).

tcf(c_94393,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),one_one_nat) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_608]) ).

tcf(c_94394,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),pls) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_524]) ).

tcf(c_94396,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_347]) ).

tcf(c_94397,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),one_one_int) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_346]) ).

tcf(c_94398,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_93345,c_254]) ).

tcf(c_94399,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),number_number_of_int(X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(demodulation,[status(thm)],[c_79931,c_94398]) ).

tcf(c_94474,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_255,c_93373]) ).

tcf(c_94477,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X0)) = hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_46106]) ).

tcf(c_94478,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_93373,c_46104]) ).

tcf(c_94479,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),pls) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_880]) ).

tcf(c_94480,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_608]) ).

tcf(c_94481,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),pls) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_524]) ).

tcf(c_94483,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_347]) ).

tcf(c_94484,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_346]) ).

tcf(c_94485,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93373,c_254]) ).

tcf(c_94486,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK30(iPr_def_19)) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(demodulation,[status(thm)],[c_79957,c_94485]) ).

tcf(c_94498,plain,
    legendre(pls,m) = pls,
    inference(superposition,[status(thm)],[c_76363,c_90020]) ).

tcf(c_94499,plain,
    legendre(m,m) = pls,
    inference(superposition,[status(thm)],[c_76934,c_90020]) ).

tcf(c_94503,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),iPr_def_11))) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_93930,c_253]) ).

tcf(c_94507,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(times_times_int(pls),hAPP_int_int(iPr_def_12,pls)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_94503]) ).

tcf(c_94508,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(iPr_def_12,one_one_int)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_94503]) ).

tcf(c_94509,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_94503]) ).

tcf(c_94510,plain,
    hAPP_int_int(times_times_int(one_one_int),iPr_def_14) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_94508,c_59638]) ).

tcf(c_94511,plain,
    ( ( zero_zero_nat = iPr_def_11 )
    | ( hAPP_int_int(times_times_int(pls),one_one_int) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_94507,c_77245]) ).

tcf(c_94512,plain,
    hAPP_int_int(times_times_int(pls),one_one_int) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_94511,c_78498]) ).

tcf(c_94528,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0)))) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_93924,c_90801]) ).

tcf(c_94529,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X1)))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_94528]) ).

tcf(c_94532,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(X0),X1)))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_94528]) ).

tcf(c_94535,plain,
    hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(s),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82935,c_94528]) ).

tcf(c_94536,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82861,c_94528]) ).

tcf(c_94537,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_94528]) ).

tcf(c_94538,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_94528]) ).

tcf(c_94541,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,number_number_of_int(hAPP_int_int(times_times_int(X0),X0))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_94528]) ).

tcf(c_94542,plain,
    hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(pls),hAPP_int_int(iPr_def_12,pls))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1001,c_94528]) ).

tcf(c_94543,plain,
    hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(min),hAPP_int_int(iPr_def_12,one_one_int))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79464,c_94528]) ).

tcf(c_94544,plain,
    hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(m),hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,m)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_76855,c_94528]) ).

tcf(c_94545,plain,
    hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_94528]) ).

tcf(c_94546,plain,
    hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,m)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_94528]) ).

tcf(c_94547,plain,
    hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(min),iPr_def_14)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_94543,c_59638]) ).

tcf(c_94548,plain,
    hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(pls),one_one_int)) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_94542,c_77245]) ).

tcf(c_94550,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0)))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_94541,c_82908]) ).

tcf(c_94551,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_94538,c_90904]) ).

tcf(c_94558,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_93822]) ).

tcf(c_94559,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_93822]) ).

tcf(c_94560,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_93822]) ).

tcf(c_94561,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_93822]) ).

tcf(c_94563,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_93822]) ).

tcf(c_94564,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_93822]) ).

tcf(c_94566,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_93822]) ).

tcf(c_94567,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_93822]) ).

tcf(c_94568,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_93822]) ).

tcf(c_94569,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_93822]) ).

tcf(c_94570,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_93822]) ).

tcf(c_94571,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_93822]) ).

tcf(c_94572,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_93822]) ).

tcf(c_94573,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_93822]) ).

tcf(c_94574,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_93822]) ).

tcf(c_94575,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_93822]) ).

tcf(c_94576,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_93822]) ).

tcf(c_94577,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_93822]) ).

tcf(c_94578,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_93822]) ).

tcf(c_94579,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_93822]) ).

tcf(c_94580,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_93822]) ).

tcf(c_94581,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_93822]) ).

tcf(c_94584,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_92656]) ).

tcf(c_94585,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_93822,c_255]) ).

tcf(c_94587,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93822,c_256]) ).

tcf(c_94589,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_93822]) ).

tcf(c_94590,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_93551]) ).

tcf(c_94591,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93822,c_79918]) ).

tcf(c_94592,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94563,c_59636]) ).

tcf(c_94593,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94558,c_79190]) ).

tcf(c_94594,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94591,c_76415]) ).

tcf(c_94595,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94566,c_76855,c_93903]) ).

tcf(c_94657,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_94594]) ).

tcf(c_94658,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_94594]) ).

tcf(c_94659,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_94594]) ).

tcf(c_94660,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_94594]) ).

tcf(c_94662,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_94594]) ).

tcf(c_94663,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_94594]) ).

tcf(c_94665,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_94594]) ).

tcf(c_94666,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_94594]) ).

tcf(c_94667,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_94594]) ).

tcf(c_94668,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_94594]) ).

tcf(c_94669,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_94594]) ).

tcf(c_94670,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_94594]) ).

tcf(c_94671,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_94594]) ).

tcf(c_94672,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_94594]) ).

tcf(c_94673,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_94594]) ).

tcf(c_94674,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_94594]) ).

tcf(c_94675,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_94594]) ).

tcf(c_94676,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_94594]) ).

tcf(c_94677,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_94594]) ).

tcf(c_94678,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_94594]) ).

tcf(c_94679,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_94594]) ).

tcf(c_94680,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_94594]) ).

tcf(c_94681,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_94594]) ).

tcf(c_94684,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_92656]) ).

tcf(c_94685,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_94594,c_255]) ).

tcf(c_94687,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94594,c_256]) ).

tcf(c_94689,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_94594]) ).

tcf(c_94690,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_93822]) ).

tcf(c_94691,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_93551]) ).

tcf(c_94692,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94594,c_79918]) ).

tcf(c_94693,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94662,c_59636]) ).

tcf(c_94694,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94657,c_79190]) ).

tcf(c_94695,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94692,c_76415]) ).

tcf(c_94696,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_94665,c_76855,c_93903]) ).

tcf(c_94773,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_92656]) ).

tcf(c_94774,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_94573,c_255]) ).

tcf(c_94776,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94573,c_256]) ).

tcf(c_94778,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_94594]) ).

tcf(c_94779,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_93822]) ).

tcf(c_94780,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_93551]) ).

tcf(c_94781,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94573,c_79918]) ).

tcf(c_94794,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_82839,c_533]) ).

tcf(c_94797,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_533,c_970]) ).

tcf(c_94807,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1)))),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X1)),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_237,c_550]) ).

tcf(c_94808,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X1))),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X1)),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_240,c_550]) ).

tcf(c_94810,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_14792,c_550]) ).

tcf(c_94811,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_373,c_550]) ).

tcf(c_94812,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_389,c_550]) ).

tcf(c_94815,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X0),X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_550,c_970]) ).

tcf(c_94839,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X1)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X0),X1)))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_237,c_551]) ).

tcf(c_94840,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),X1)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X0),X1)),X1))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_240,c_551]) ).

tcf(c_94842,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_14792,c_551]) ).

tcf(c_94843,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0)),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_373,c_551]) ).

tcf(c_94844,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_389,c_551]) ).

tcf(c_94865,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),one_one_real)),hAPP_real_real(times_times_real(X0),X0))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_370,c_596]) ).

tcf(c_94866,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_14792,c_596]) ).

tcf(c_94867,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X0))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_373,c_596]) ).

tcf(c_94868,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X0),iPr_def_11)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_82839,c_596]) ).

tcf(c_94869,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X1))),hAPP_real_real(times_times_real(X2),X2))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_219,c_596]) ).

tcf(c_94871,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(one_one_real),hAPP_real_real(times_times_real(X0),X0))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_325,c_596]) ).

tcf(c_94873,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(times_times_int(X0),X0))),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_383,c_596]) ).

tcf(c_94874,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(zero_zero_real),hAPP_real_real(times_times_real(X0),X0))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_1002,c_596]) ).

tcf(c_94876,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_nat_real(power_power_real(X1),iPr_def_11))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_82839,c_596]) ).

tcf(c_94877,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X1),X2)),X2)))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_219,c_596]) ).

tcf(c_94879,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),one_one_real)),zero_zero_real)),
    inference(superposition,[status(thm)],[c_325,c_596]) ).

tcf(c_94881,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),number267125858f_real(hAPP_int_int(times_times_int(X1),X1)))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_383,c_596]) ).

tcf(c_94882,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),zero_zero_real)),zero_zero_real)),
    inference(superposition,[status(thm)],[c_1002,c_596]) ).

tcf(c_94884,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(number267125858f_real(X0)),iPr_def_11)),hAPP_real_real(times_times_real(X1),X1))),zero_zero_real)),
    inference(light_normalisation,[status(thm)],[c_94873,c_82848]) ).

tcf(c_94885,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X1)),iPr_def_11)),hAPP_real_real(times_times_real(X2),X2))),zero_zero_real)),
    inference(light_normalisation,[status(thm)],[c_94869,c_91730]) ).

tcf(c_94933,plain,
    hBOOL(hAPP_int_bool(iPr_def_19,hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59643,c_90706]) ).

tcf(c_94934,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),iPr_def_14)),
    inference(superposition,[status(thm)],[c_59638,c_90706]) ).

tcf(c_94938,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(min),min)),min)),
    inference(superposition,[status(thm)],[c_76610,c_90706]) ).

tcf(c_94940,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(superposition,[status(thm)],[c_82935,c_90706]) ).

tcf(c_94941,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_83830,c_90706]) ).

tcf(c_94942,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X0)),
    inference(superposition,[status(thm)],[c_90706,c_46112]) ).

tcf(c_94943,plain,
    ! [X0: $i] : ~ hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),d22set(X0))),
    inference(superposition,[status(thm)],[c_90706,c_1579]) ).

tcf(c_94944,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),hAPP_i1948725293t_bool(ord_less_int,X0))),
    inference(superposition,[status(thm)],[c_90706,c_226]) ).

tcf(c_94945,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_12,pls))),
    inference(superposition,[status(thm)],[c_90706,c_611]) ).

tcf(c_94952,plain,
    ! [X0: $i] : is_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_90945]) ).

tcf(c_94953,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_14),X0)),X1)),
    inference(superposition,[status(thm)],[c_253,c_90945]) ).

tcf(c_94956,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X1))),
    inference(superposition,[status(thm)],[c_217,c_90945]) ).

tcf(c_94959,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),
    inference(superposition,[status(thm)],[c_59637,c_90945]) ).

tcf(c_94962,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(iPr_def_14),X2)))),
    inference(superposition,[status(thm)],[c_217,c_90945]) ).

tcf(c_94964,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),pls)),
    inference(superposition,[status(thm)],[c_1001,c_90945]) ).

tcf(c_94965,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(superposition,[status(thm)],[c_76855,c_90945]) ).

tcf(c_94966,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),
    inference(superposition,[status(thm)],[c_79150,c_90945]) ).

tcf(c_94967,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(iPr_def_14),X2))),X0)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(iPr_def_14),X2)),
    inference(superposition,[status(thm)],[c_90945,c_46106]) ).

tcf(c_94968,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(iPr_def_14),X2)))),X0) = pls,
    inference(superposition,[status(thm)],[c_90945,c_46104]) ).

tcf(c_94969,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_880]) ).

tcf(c_94970,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),one_one_nat) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_608]) ).

tcf(c_94971,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_524]) ).

tcf(c_94972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_523]) ).

tcf(c_94973,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_347]) ).

tcf(c_94974,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))),one_one_int) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_346]) ).

tcf(c_94975,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),X1)),
    inference(superposition,[status(thm)],[c_90945,c_254]) ).

tcf(c_94990,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),
    inference(demodulation,[status(thm)],[c_94965,c_90827]) ).

tcf(c_94993,plain,
    hBOOL(member_int(one_one_int,zcong(pls,m))),
    inference(superposition,[status(thm)],[c_76934,c_91323]) ).

tcf(c_94994,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))))))),
    inference(superposition,[status(thm)],[c_79319,c_91323]) ).

tcf(c_94995,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(minus_minus_int(min),X0))),zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)))))),
    inference(superposition,[status(thm)],[c_79319,c_91323]) ).

tcf(c_94997,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0)),zcong(pls,hAPP_int_int(iPr_def_13,hAPP_int_int(minus_minus_int(min),hAPP_int_int(times_times_int(iPr_def_14),X0)))))),
    inference(light_normalisation,[status(thm)],[c_94994,c_79321]) ).

tcf(c_95000,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_94695]) ).

tcf(c_95001,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_94695]) ).

tcf(c_95002,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_94695]) ).

tcf(c_95003,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_94695]) ).

tcf(c_95005,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_94695]) ).

tcf(c_95006,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_94695]) ).

tcf(c_95008,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_94695]) ).

tcf(c_95009,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_94695]) ).

tcf(c_95010,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_94695]) ).

tcf(c_95011,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_94695]) ).

tcf(c_95012,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_94695]) ).

tcf(c_95013,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_94695]) ).

tcf(c_95014,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_94695]) ).

tcf(c_95015,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_94695]) ).

tcf(c_95016,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_94695]) ).

tcf(c_95017,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_94695]) ).

tcf(c_95018,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_94695]) ).

tcf(c_95019,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_94695]) ).

tcf(c_95020,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_94695]) ).

tcf(c_95021,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_94695]) ).

tcf(c_95022,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_94695]) ).

tcf(c_95023,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_94695]) ).

tcf(c_95024,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_94695]) ).

tcf(c_95025,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_94695]) ).

tcf(c_95026,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_94695]) ).

tcf(c_95029,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_92656]) ).

tcf(c_95030,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_94695,c_255]) ).

tcf(c_95032,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94695,c_256]) ).

tcf(c_95034,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_94695]) ).

tcf(c_95035,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_94594]) ).

tcf(c_95036,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_93822]) ).

tcf(c_95037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_93551]) ).

tcf(c_95038,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94695,c_79918]) ).

tcf(c_95039,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95005,c_59636]) ).

tcf(c_95040,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95000,c_79190]) ).

tcf(c_95041,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95038,c_76415]) ).

tcf(c_95042,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95008,c_76855,c_93903]) ).

tcf(c_95229,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_92656]) ).

tcf(c_95230,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_94672,c_255]) ).

tcf(c_95232,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94672,c_256]) ).

tcf(c_95234,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_94695]) ).

tcf(c_95235,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_94594]) ).

tcf(c_95236,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_93822]) ).

tcf(c_95237,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_93551]) ).

tcf(c_95238,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94672,c_79918]) ).

tcf(c_95242,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_95041]) ).

tcf(c_95243,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_95041]) ).

tcf(c_95244,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_95041]) ).

tcf(c_95245,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_95041]) ).

tcf(c_95247,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_95041]) ).

tcf(c_95248,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_95041]) ).

tcf(c_95250,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_95041]) ).

tcf(c_95251,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_95041]) ).

tcf(c_95252,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_95041]) ).

tcf(c_95253,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_95041]) ).

tcf(c_95254,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_95041]) ).

tcf(c_95255,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_95041]) ).

tcf(c_95256,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_95041]) ).

tcf(c_95257,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_95041]) ).

tcf(c_95258,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_95041]) ).

tcf(c_95259,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_95041]) ).

tcf(c_95260,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_95041]) ).

tcf(c_95261,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_95041]) ).

tcf(c_95262,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_95041]) ).

tcf(c_95263,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_95041]) ).

tcf(c_95264,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_95041]) ).

tcf(c_95265,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_95041]) ).

tcf(c_95266,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_95041]) ).

tcf(c_95267,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_95041]) ).

tcf(c_95268,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_95041]) ).

tcf(c_95269,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_95041]) ).

tcf(c_95270,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_95041]) ).

tcf(c_95273,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_92656]) ).

tcf(c_95274,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_95041,c_255]) ).

tcf(c_95276,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95041,c_256]) ).

tcf(c_95278,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_95041]) ).

tcf(c_95279,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_94695]) ).

tcf(c_95280,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_94594]) ).

tcf(c_95281,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_93822]) ).

tcf(c_95282,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_93551]) ).

tcf(c_95283,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95041,c_79918]) ).

tcf(c_95284,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95247,c_59636]) ).

tcf(c_95285,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95242,c_79190]) ).

tcf(c_95286,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95283,c_76415]) ).

tcf(c_95287,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95250,c_76855,c_93903]) ).

tcf(c_95353,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_92656]) ).

tcf(c_95354,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_95015,c_255]) ).

tcf(c_95356,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95015,c_256]) ).

tcf(c_95358,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_95041]) ).

tcf(c_95359,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_94695]) ).

tcf(c_95360,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_94594]) ).

tcf(c_95361,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_93822]) ).

tcf(c_95362,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_93551]) ).

tcf(c_95363,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95015,c_79918]) ).

tcf(c_95367,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_95286]) ).

tcf(c_95368,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_95286]) ).

tcf(c_95369,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_95286]) ).

tcf(c_95370,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_95286]) ).

tcf(c_95372,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_95286]) ).

tcf(c_95373,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_95286]) ).

tcf(c_95375,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_95286]) ).

tcf(c_95376,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_95286]) ).

tcf(c_95377,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_95286]) ).

tcf(c_95378,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_95286]) ).

tcf(c_95379,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_95286]) ).

tcf(c_95380,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_95286]) ).

tcf(c_95381,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_95286]) ).

tcf(c_95382,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_95286]) ).

tcf(c_95383,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_95286]) ).

tcf(c_95384,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_95286]) ).

tcf(c_95385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_95286]) ).

tcf(c_95386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_95286]) ).

tcf(c_95387,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_95286]) ).

tcf(c_95388,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_95286]) ).

tcf(c_95389,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_95286]) ).

tcf(c_95390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_95286]) ).

tcf(c_95391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_95286]) ).

tcf(c_95392,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_95286]) ).

tcf(c_95393,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_95286]) ).

tcf(c_95394,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_95286]) ).

tcf(c_95395,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_95286]) ).

tcf(c_95396,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_95286]) ).

tcf(c_95397,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_95286]) ).

tcf(c_95400,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_92656]) ).

tcf(c_95401,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_95286,c_255]) ).

tcf(c_95403,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95286,c_256]) ).

tcf(c_95405,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_95286]) ).

tcf(c_95406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_95041]) ).

tcf(c_95407,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_94695]) ).

tcf(c_95408,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_94594]) ).

tcf(c_95409,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_93822]) ).

tcf(c_95410,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_93551]) ).

tcf(c_95411,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95286,c_79918]) ).

tcf(c_95412,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95372,c_59636]) ).

tcf(c_95413,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95367,c_79190]) ).

tcf(c_95414,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95411,c_76415]) ).

tcf(c_95415,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95375,c_76855,c_93903]) ).

tcf(c_95530,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_92656]) ).

tcf(c_95531,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_95257,c_255]) ).

tcf(c_95533,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95257,c_256]) ).

tcf(c_95535,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_95286]) ).

tcf(c_95536,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_95041]) ).

tcf(c_95537,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_94695]) ).

tcf(c_95538,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_94594]) ).

tcf(c_95539,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_93822]) ).

tcf(c_95540,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_93551]) ).

tcf(c_95541,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95257,c_79918]) ).

tcf(c_95558,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_95414]) ).

tcf(c_95559,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_95414]) ).

tcf(c_95560,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_95414]) ).

tcf(c_95561,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_95414]) ).

tcf(c_95563,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_95414]) ).

tcf(c_95564,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_95414]) ).

tcf(c_95566,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_95414]) ).

tcf(c_95567,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_95414]) ).

tcf(c_95568,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_95414]) ).

tcf(c_95569,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_95414]) ).

tcf(c_95570,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_95414]) ).

tcf(c_95571,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_95414]) ).

tcf(c_95572,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_95414]) ).

tcf(c_95573,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_95414]) ).

tcf(c_95574,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_95414]) ).

tcf(c_95575,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_95414]) ).

tcf(c_95576,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_95414]) ).

tcf(c_95577,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_95414]) ).

tcf(c_95578,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_95414]) ).

tcf(c_95579,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_95414]) ).

tcf(c_95580,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_95414]) ).

tcf(c_95581,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_95414]) ).

tcf(c_95582,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_95414]) ).

tcf(c_95583,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_95414]) ).

tcf(c_95584,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_95414]) ).

tcf(c_95585,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_95414]) ).

tcf(c_95586,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_95414]) ).

tcf(c_95587,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_95414]) ).

tcf(c_95588,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_95414]) ).

tcf(c_95589,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_95414]) ).

tcf(c_95590,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_95414]) ).

tcf(c_95593,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_92656]) ).

tcf(c_95594,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_95414,c_255]) ).

tcf(c_95596,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95414,c_256]) ).

tcf(c_95598,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_95414]) ).

tcf(c_95599,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_95286]) ).

tcf(c_95600,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_95041]) ).

tcf(c_95601,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_94695]) ).

tcf(c_95602,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_94594]) ).

tcf(c_95603,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_93822]) ).

tcf(c_95604,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_93551]) ).

tcf(c_95605,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95414,c_79918]) ).

tcf(c_95606,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95563,c_59636]) ).

tcf(c_95607,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95558,c_79190]) ).

tcf(c_95608,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95605,c_76415]) ).

tcf(c_95609,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_95566,c_76855,c_93903]) ).

tcf(c_95671,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_92656]) ).

tcf(c_95672,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_95382,c_255]) ).

tcf(c_95674,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95382,c_256]) ).

tcf(c_95676,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_95414]) ).

tcf(c_95677,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_95286]) ).

tcf(c_95678,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_95041]) ).

tcf(c_95679,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_94695]) ).

tcf(c_95680,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_94594]) ).

tcf(c_95681,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_93822]) ).

tcf(c_95682,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_93551]) ).

tcf(c_95683,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95382,c_79918]) ).

tcf(c_95702,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(light_normalisation,[status(thm)],[c_634,c_59636]) ).

tcf(c_95709,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59638,c_95702]) ).

tcf(c_95710,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_15))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_59639,c_95702]) ).

tcf(c_95711,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_16))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_59640,c_95702]) ).

tcf(c_95712,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_18))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_59642,c_95702]) ).

tcf(c_95713,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(min),min))) ),
    inference(superposition,[status(thm)],[c_76610,c_95702]) ).

tcf(c_95715,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(s),s))) ),
    inference(superposition,[status(thm)],[c_82935,c_95702]) ).

tcf(c_95716,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK30(iPr_def_19)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int))) ),
    inference(superposition,[status(thm)],[c_83830,c_95702]) ).

tcf(c_95717,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),pls)) ),
    inference(superposition,[status(thm)],[c_95702,c_46112]) ).

tcf(c_95718,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),d22set(pls))) ),
    inference(superposition,[status(thm)],[c_95702,c_1579]) ).

tcf(c_95719,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(iPr_def_12,X0),hAPP_i1948725293t_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_95702,c_226]) ).

tcf(c_95720,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_95702,c_611]) ).

tcf(c_95725,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_15)),
    inference(forward_subsumption_resolution,[status(thm)],[c_95710,c_76717]) ).

tcf(c_95726,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_14)),
    inference(forward_subsumption_resolution,[status(thm)],[c_95709,c_846]) ).

tcf(c_95735,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(min),min))),
    inference(forward_subsumption_resolution,[status(thm)],[c_95713,c_764]) ).

tcf(c_95738,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_95715,c_1135]) ).

tcf(c_95743,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_nat(power_power_nat(X0),X1),
    inference(superposition,[status(thm)],[c_610,c_674]) ).

tcf(c_95744,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) ) ),
    inference(superposition,[status(thm)],[c_1063,c_674]) ).

tcf(c_95745,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(zero_zero_nat),X1)) = hAPP_nat_nat(power_power_nat(one_one_nat),X1),
    inference(superposition,[status(thm)],[c_1223,c_674]) ).

tcf(c_95746,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(one_one_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(power_power_nat(one_one_nat),X1),
    inference(superposition,[status(thm)],[c_1222,c_674]) ).

tcf(c_95747,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X0)),X1) = hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),
    inference(superposition,[status(thm)],[c_82316,c_674]) ).

tcf(c_95748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_674,c_674]) ).

tcf(c_95749,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(power_power_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_674,c_1065]) ).

tcf(c_95750,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),one_one_nat)) = hAPP_nat_nat(power_power_nat(X0),X1),
    inference(superposition,[status(thm)],[c_674,c_610]) ).

tcf(c_95751,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat)) = one_one_nat,
    inference(superposition,[status(thm)],[c_674,c_1223]) ).

tcf(c_95782,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_real(power_power_real(X0),X1),
    inference(superposition,[status(thm)],[c_609,c_675]) ).

tcf(c_95783,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_real(power_power_real(zero_zero_real),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_real(power_power_real(zero_zero_real),X1) ) ),
    inference(superposition,[status(thm)],[c_495,c_675]) ).

tcf(c_95784,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(zero_zero_nat),X1)) = hAPP_nat_real(power_power_real(one_one_real),X1),
    inference(superposition,[status(thm)],[c_782,c_675]) ).

tcf(c_95785,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(one_one_real),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_real(power_power_real(one_one_real),X1),
    inference(superposition,[status(thm)],[c_671,c_675]) ).

tcf(c_95786,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X0)),X1) = hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),
    inference(superposition,[status(thm)],[c_82839,c_675]) ).

tcf(c_95787,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X1)) = hAPP_nat_real(power_power_real(one_one_real),X1),
    inference(superposition,[status(thm)],[c_85145,c_675]) ).

tcf(c_95788,plain,
    ! [X0: $i] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)) = hAPP_nat_real(power_power_real(one_one_real),X0),
    inference(superposition,[status(thm)],[c_85148,c_675]) ).

tcf(c_95789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_675,c_675]) ).

tcf(c_95790,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(superposition,[status(thm)],[c_675,c_533]) ).

tcf(c_95791,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(superposition,[status(thm)],[c_675,c_527]) ).

tcf(c_95792,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_real(power_power_real(X0),X1) = zero_zero_real )
      | ( hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_675,c_489]) ).

tcf(c_95793,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),one_one_nat)) = hAPP_nat_real(power_power_real(X0),X1),
    inference(superposition,[status(thm)],[c_675,c_609]) ).

tcf(c_95794,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat)) = one_one_real,
    inference(superposition,[status(thm)],[c_675,c_782]) ).

tcf(c_95795,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_675,c_81997]) ).

tcf(c_95882,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_int(power_power_int(pls),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_int(power_power_int(pls),X1) ) ),
    inference(superposition,[status(thm)],[c_491,c_676]) ).

tcf(c_95883,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(zero_zero_nat),X1)) = hAPP_nat_int(power_power_int(one_one_int),X1),
    inference(superposition,[status(thm)],[c_784,c_676]) ).

tcf(c_95884,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(one_one_int),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_int(power_power_int(one_one_int),X1),
    inference(superposition,[status(thm)],[c_673,c_676]) ).

tcf(c_95885,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(pls),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(pls),X0),
    inference(superposition,[status(thm)],[c_77288,c_676]) ).

tcf(c_95886,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X0)),X1) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),
    inference(superposition,[status(thm)],[c_82861,c_676]) ).

tcf(c_95887,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(undefined_int(int)),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(undefined_int(int)),X0),
    inference(superposition,[status(thm)],[c_77289,c_676]) ).

tcf(c_95888,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(min),X0),
    inference(superposition,[status(thm)],[c_77292,c_676]) ).

tcf(c_95889,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(twoSqu1241645765sum2sq(X0)),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_int(power_power_int(twoSqu1241645765sum2sq(X0)),X1),
    inference(superposition,[status(thm)],[c_77295,c_676]) ).

tcf(c_95890,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(m),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(m),X0),
    inference(superposition,[status(thm)],[c_77299,c_676]) ).

tcf(c_95891,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(s1),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(s1),X0),
    inference(superposition,[status(thm)],[c_77300,c_676]) ).

tcf(c_95892,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(s),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(s),X0),
    inference(superposition,[status(thm)],[c_77301,c_676]) ).

tcf(c_95893,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(t),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(t),X0),
    inference(superposition,[status(thm)],[c_77302,c_676]) ).

tcf(c_95894,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK9),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK9),X0),
    inference(superposition,[status(thm)],[c_77303,c_676]) ).

tcf(c_95895,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK10),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK10),X0),
    inference(superposition,[status(thm)],[c_77304,c_676]) ).

tcf(c_95896,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK11),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK11),X0),
    inference(superposition,[status(thm)],[c_77305,c_676]) ).

tcf(c_95897,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK13),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK13),X0),
    inference(superposition,[status(thm)],[c_77306,c_676]) ).

tcf(c_95898,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(iPr_def_14),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(iPr_def_14),X0),
    inference(superposition,[status(thm)],[c_77311,c_676]) ).

tcf(c_95899,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(iPr_def_15),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(iPr_def_15),X0),
    inference(superposition,[status(thm)],[c_77312,c_676]) ).

tcf(c_95900,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(iPr_def_16),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(iPr_def_16),X0),
    inference(superposition,[status(thm)],[c_77313,c_676]) ).

tcf(c_95901,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(iPr_def_17),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(iPr_def_17),X0),
    inference(superposition,[status(thm)],[c_77314,c_676]) ).

tcf(c_95902,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(iPr_def_18),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(iPr_def_18),X0),
    inference(superposition,[status(thm)],[c_77315,c_676]) ).

tcf(c_95903,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_77316,c_676]) ).

tcf(c_95904,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X1)) = hAPP_nat_int(power_power_int(one_one_int),X1),
    inference(superposition,[status(thm)],[c_85131,c_676]) ).

tcf(c_95905,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0),
    inference(superposition,[status(thm)],[c_88497,c_676]) ).

tcf(c_95906,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88516,c_676]) ).

tcf(c_95907,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1),
    inference(superposition,[status(thm)],[c_88553,c_676]) ).

tcf(c_95908,plain,
    ! [X0: $i,X1: $i,X2: $i] : number_number_of_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)),
    inference(superposition,[status(thm)],[c_676,c_76401]) ).

tcf(c_95909,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))),
    inference(superposition,[status(thm)],[c_676,c_67]) ).

tcf(c_95910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_676,c_676]) ).

tcf(c_95911,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(X0),X1) = pls )
      | ~ is_int(hAPP_nat_int(power_power_int(X0),X1))
      | ( hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != pls ) ),
    inference(superposition,[status(thm)],[c_676,c_488]) ).

tcf(c_95912,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat)) = one_one_int,
    inference(superposition,[status(thm)],[c_676,c_784]) ).

tcf(c_95913,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_94503]) ).

tcf(c_95914,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_83839]) ).

tcf(c_95915,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_83271]) ).

tcf(c_95916,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_82919]) ).

tcf(c_95917,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_676,c_81992]) ).

tcf(c_95918,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_79175]) ).

tcf(c_95919,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X0),X1)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_676,c_79141]) ).

tcf(c_95921,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_78501]) ).

tcf(c_95922,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_76355]) ).

tcf(c_95923,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_59645]) ).

tcf(c_95924,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_82918]) ).

tcf(c_95925,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_59645]) ).

tcf(c_95946,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(X0),X1) = pls )
      | ( hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != pls ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_95911,c_67]) ).

tcf(c_95997,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_15),pls)),
    inference(superposition,[status(thm)],[c_95725,c_46112]) ).

tcf(c_95998,plain,
    ~ hBOOL(member_int(iPr_def_15,d22set(pls))),
    inference(superposition,[status(thm)],[c_95725,c_1579]) ).

tcf(c_95999,plain,
    hBOOL(member_int(iPr_def_15,hAPP_i1948725293t_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_95725,c_226]) ).

tcf(c_96000,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_15)),
    inference(superposition,[status(thm)],[c_95725,c_611]) ).

tcf(c_96001,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14),pls)),
    inference(superposition,[status(thm)],[c_95726,c_46112]) ).

tcf(c_96002,plain,
    ~ hBOOL(member_int(iPr_def_14,d22set(pls))),
    inference(superposition,[status(thm)],[c_95726,c_1579]) ).

tcf(c_96003,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(ord_less_int,pls))),
    inference(superposition,[status(thm)],[c_95726,c_226]) ).

tcf(c_96004,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_14)),
    inference(superposition,[status(thm)],[c_95726,c_611]) ).

tcf(c_96011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95923]) ).

tcf(c_96012,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95923]) ).

tcf(c_96015,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95923]) ).

tcf(c_96018,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),zero_zero_nat)),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95923]) ).

tcf(c_96019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95923]) ).

tcf(c_96020,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95923]) ).

tcf(c_96021,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_95923]) ).

tcf(c_96024,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96020,c_78498]) ).

tcf(c_96043,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95925]) ).

tcf(c_96044,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_95925]) ).

tcf(c_96046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95925]) ).

tcf(c_96047,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95925]) ).

tcf(c_96050,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95925]) ).

tcf(c_96053,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95925]) ).

tcf(c_96057,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96043,c_78498]) ).

tcf(c_96062,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95918]) ).

tcf(c_96063,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(iPr_def_14),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95918]) ).

tcf(c_96066,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95918]) ).

tcf(c_96069,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95918]) ).

tcf(c_96083,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)))),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_95916]) ).

tcf(c_96084,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_int_int(times_times_int(X3),X3)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95916]) ).

tcf(c_96085,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95916]) ).

tcf(c_96088,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95916]) ).

tcf(c_96091,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),zero_zero_nat)),hAPP_int_int(times_times_int(X1),X1)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95916]) ).

tcf(c_96093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X3),hAPP_int_int(times_times_int(X2),X3)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_95916]) ).

tcf(c_96094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X2),X3)),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_95916]) ).

tcf(c_96097,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),number_number_of_int(hAPP_int_int(times_times_int(X2),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_95916]) ).

tcf(c_96101,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_95916]) ).

tcf(c_96102,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_95916]) ).

tcf(c_96104,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(X0),X0) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_96085,c_83223]) ).

tcf(c_96124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_95924]) ).

tcf(c_96125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_95924]) ).

tcf(c_96128,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_95924]) ).

tcf(c_96132,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_95924]) ).

tcf(c_96134,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95924]) ).

tcf(c_96135,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95924]) ).

tcf(c_96138,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95924]) ).

tcf(c_96141,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95924]) ).

tcf(c_96144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_96125,c_90904]) ).

tcf(c_96165,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X1) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96015]) ).

tcf(c_96169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96015]) ).

tcf(c_96174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96015]) ).

tcf(c_96175,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96015]) ).

tcf(c_96176,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96015]) ).

tcf(c_96178,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96175,c_78498]) ).

tcf(c_96185,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_83521,c_83527]) ).

tcf(c_96186,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_96185,c_253,c_79918,c_90977,c_91937]) ).

tcf(c_96187,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93822,c_96186]) ).

tcf(c_96188,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94573,c_96186]) ).

tcf(c_96189,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94594,c_96186]) ).

tcf(c_96190,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94672,c_96186]) ).

tcf(c_96191,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94695,c_96186]) ).

tcf(c_96192,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95015,c_96186]) ).

tcf(c_96193,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95041,c_96186]) ).

tcf(c_96194,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95257,c_96186]) ).

tcf(c_96195,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95286,c_96186]) ).

tcf(c_96196,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95382,c_96186]) ).

tcf(c_96197,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95414,c_96186]) ).

tcf(c_96199,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_96186]) ).

tcf(c_96201,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_96186]) ).

tcf(c_96202,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_96186]) ).

tcf(c_96204,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_96186]) ).

tcf(c_96205,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_96186]) ).

tcf(c_96206,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_96186]) ).

tcf(c_96207,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_96186]) ).

tcf(c_96209,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96186,c_93890]) ).

tcf(c_96210,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_96186,c_1042]) ).

tcf(c_96211,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = pls,
    inference(superposition,[status(thm)],[c_96186,c_92002]) ).

tcf(c_96212,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1),
    inference(superposition,[status(thm)],[c_96186,c_252]) ).

tcf(c_96213,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0))))),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_96186,c_833]) ).

tcf(c_96215,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_96186,c_76535]) ).

tcf(c_96216,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_96186,c_76498]) ).

tcf(c_96217,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_96186,c_1045]) ).

tcf(c_96218,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X1))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_96186,c_217]) ).

tcf(c_96220,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X1)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_96186,c_833]) ).

tcf(c_96337,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X0),X1))) ),
    inference(superposition,[status(thm)],[c_675,c_698]) ).

tcf(c_96340,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0)) ),
    inference(superposition,[status(thm)],[c_782,c_698]) ).

tcf(c_96342,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(times_times_real(X0),X0)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0)) ),
    inference(superposition,[status(thm)],[c_82839,c_698]) ).

tcf(c_96343,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),one_one_real))
    | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(min))) ),
    inference(superposition,[status(thm)],[c_85145,c_698]) ).

tcf(c_96355,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_674,c_699]) ).

tcf(c_96358,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1223,c_699]) ).

tcf(c_96360,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(times_times_nat(X0),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_82316,c_699]) ).

tcf(c_96361,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(power_power_nat(X0),X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_699,c_1332]) ).

tcf(c_96379,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_676,c_700]) ).

tcf(c_96381,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_784,c_700]) ).

tcf(c_96384,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_82861,c_700]) ).

tcf(c_96406,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_nat_int(power_power_int(X0),X1),hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_700,c_226]) ).

tcf(c_96408,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK27(X1,hAPP_nat_int(power_power_int(X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_700,c_46404]) ).

tcf(c_96422,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_674,c_741]) ).

tcf(c_96427,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_82316,c_741]) ).

tcf(c_96428,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_741,c_1693]) ).

tcf(c_96429,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_741,c_1364]) ).

tcf(c_96439,plain,
    hBOOL(member_int(iPr_def_15,hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),
    inference(superposition,[status(thm)],[c_96000,c_226]) ).

tcf(c_96441,plain,
    ! [X0: $i] : is_int(sK27(X0,iPr_def_15)),
    inference(superposition,[status(thm)],[c_96000,c_46404]) ).

tcf(c_96443,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,iPr_def_15)),X0)) = sK27(X1,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_46106]) ).

tcf(c_96444,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,iPr_def_15))),X0) = pls,
    inference(superposition,[status(thm)],[c_96441,c_46104]) ).

tcf(c_96445,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK27(X0,iPr_def_15)),pls) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_880]) ).

tcf(c_96446,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK27(X0,iPr_def_15)),one_one_nat) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_608]) ).

tcf(c_96447,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK27(X0,iPr_def_15)),pls) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_524]) ).

tcf(c_96448,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK27(X0,iPr_def_15)) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_523]) ).

tcf(c_96449,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK27(X0,iPr_def_15)) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_347]) ).

tcf(c_96450,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK27(X0,iPr_def_15)),one_one_int) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_346]) ).

tcf(c_96451,plain,
    ! [X0: $i] : number_number_of_int(sK27(X0,iPr_def_15)) = sK27(X0,iPr_def_15),
    inference(superposition,[status(thm)],[c_96441,c_254]) ).

tcf(c_96465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96050]) ).

tcf(c_96466,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96050]) ).

tcf(c_96467,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96050]) ).

tcf(c_96470,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X1) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96050]) ).

tcf(c_96474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96050]) ).

tcf(c_96479,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_96467,c_59636]) ).

tcf(c_96482,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96466,c_78498]) ).

tcf(c_96506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),hAPP_nat_int(power_power_int(X4),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96011]) ).

tcf(c_96507,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96011]) ).

tcf(c_96510,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96011]) ).

tcf(c_96514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),X2))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96011]) ).

tcf(c_96520,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96011]) ).

tcf(c_96521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96011]) ).

tcf(c_96522,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96011]) ).

tcf(c_96523,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96011]) ).

tcf(c_96526,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96522,c_78498]) ).

tcf(c_96604,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),zero_zero_nat)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96019]) ).

tcf(c_96605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96019]) ).

tcf(c_96612,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96019]) ).

tcf(c_96619,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96046]) ).

tcf(c_96620,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96046]) ).

tcf(c_96622,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96046]) ).

tcf(c_96623,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96046]) ).

tcf(c_96626,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96046]) ).

tcf(c_96630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96046]) ).

tcf(c_96636,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),zero_zero_nat))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96046]) ).

tcf(c_96637,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_96620,c_59636]) ).

tcf(c_96640,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_96619,c_78498]) ).

tcf(c_96673,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(iPr_def_12,pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95922]) ).

tcf(c_96679,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95922]) ).

tcf(c_96681,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),iPr_def_11) = zero_zero_nat )
      | ( one_one_int != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_96673,c_77245]) ).

tcf(c_96683,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_93551,c_83524]) ).

tcf(c_96684,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_93822,c_83524]) ).

tcf(c_96685,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_94573,c_83524]) ).

tcf(c_96686,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_94594,c_83524]) ).

tcf(c_96687,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_94672,c_83524]) ).

tcf(c_96688,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_94695,c_83524]) ).

tcf(c_96689,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95015,c_83524]) ).

tcf(c_96690,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95041,c_83524]) ).

tcf(c_96691,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95257,c_83524]) ).

tcf(c_96692,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95286,c_83524]) ).

tcf(c_96693,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95382,c_83524]) ).

tcf(c_96694,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95414,c_83524]) ).

tcf(c_96695,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),pls)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),pls)),X0)),
    inference(superposition,[status(thm)],[c_574,c_83524]) ).

tcf(c_96696,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),min)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),min)),X0)),
    inference(superposition,[status(thm)],[c_76397,c_83524]) ).

tcf(c_96697,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),one_one_int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),one_one_int)),X0)),
    inference(superposition,[status(thm)],[c_76393,c_83524]) ).

tcf(c_96698,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),undefined_int(int))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),undefined_int(int))),X0)),
    inference(superposition,[status(thm)],[c_76395,c_83524]) ).

tcf(c_96699,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))),X1)),
    inference(superposition,[status(thm)],[c_76399,c_83524]) ).

tcf(c_96700,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))),X2)),
    inference(superposition,[status(thm)],[c_76401,c_83524]) ).

tcf(c_96701,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),m)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),m)),X0)),
    inference(superposition,[status(thm)],[c_76402,c_83524]) ).

tcf(c_96702,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),s1)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),s1)),X0)),
    inference(superposition,[status(thm)],[c_76403,c_83524]) ).

tcf(c_96703,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),s)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),s)),X0)),
    inference(superposition,[status(thm)],[c_76404,c_83524]) ).

tcf(c_96704,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),t)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),t)),X0)),
    inference(superposition,[status(thm)],[c_76405,c_83524]) ).

tcf(c_96705,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK9)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK9)),X0)),
    inference(superposition,[status(thm)],[c_76406,c_83524]) ).

tcf(c_96706,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK10)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK10)),X0)),
    inference(superposition,[status(thm)],[c_76407,c_83524]) ).

tcf(c_96707,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK11)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK11)),X0)),
    inference(superposition,[status(thm)],[c_76408,c_83524]) ).

tcf(c_96708,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK13)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK13)),X0)),
    inference(superposition,[status(thm)],[c_76409,c_83524]) ).

tcf(c_96709,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_14)),X0)),
    inference(superposition,[status(thm)],[c_76410,c_83524]) ).

tcf(c_96710,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_15)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_15)),X0)),
    inference(superposition,[status(thm)],[c_76411,c_83524]) ).

tcf(c_96711,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_16)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_16)),X0)),
    inference(superposition,[status(thm)],[c_76412,c_83524]) ).

tcf(c_96712,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_17)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_17)),X0)),
    inference(superposition,[status(thm)],[c_76413,c_83524]) ).

tcf(c_96713,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_18)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),iPr_def_18)),X0)),
    inference(superposition,[status(thm)],[c_76414,c_83524]) ).

tcf(c_96714,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_76415,c_83524]) ).

tcf(c_96715,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),X1)),
    inference(superposition,[status(thm)],[c_77366,c_83524]) ).

tcf(c_96716,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),X0)),
    inference(superposition,[status(thm)],[c_78203,c_83524]) ).

tcf(c_96717,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_79573,c_83524]) ).

tcf(c_96718,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_79414,c_83524]) ).

tcf(c_96719,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79557,c_83524]) ).

tcf(c_96720,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79437,c_83524]) ).

tcf(c_96721,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X0))),X1)),
    inference(superposition,[status(thm)],[c_79918,c_83524]) ).

tcf(c_96722,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),m))),X1)),
    inference(superposition,[status(thm)],[c_83504,c_83524]) ).

tcf(c_96723,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X0))),X1)),
    inference(superposition,[status(thm)],[c_80664,c_83524]) ).

tcf(c_96724,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_80677,c_83524]) ).

tcf(c_96725,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),m))),X1)),
    inference(superposition,[status(thm)],[c_80692,c_83524]) ).

tcf(c_96726,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_80705,c_83524]) ).

tcf(c_96727,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X0)),
    inference(superposition,[status(thm)],[c_88502,c_83524]) ).

tcf(c_96728,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_88521,c_83524]) ).

tcf(c_96729,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_88558,c_83524]) ).

tcf(c_96730,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),pls) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),pls)),
    inference(superposition,[status(thm)],[c_574,c_83524]) ).

tcf(c_96731,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),min) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),min)),
    inference(superposition,[status(thm)],[c_76397,c_83524]) ).

tcf(c_96732,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),one_one_int) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_83524]) ).

tcf(c_96733,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),undefined_int(int)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_83524]) ).

tcf(c_96734,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),twoSqu1241645765sum2sq(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_83524]) ).

tcf(c_96735,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(X1,X2)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_83524]) ).

tcf(c_96736,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),m) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),m)),
    inference(superposition,[status(thm)],[c_76402,c_83524]) ).

tcf(c_96737,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),s1) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_83524]) ).

tcf(c_96738,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),s) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),s)),
    inference(superposition,[status(thm)],[c_76404,c_83524]) ).

tcf(c_96739,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),t) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),t)),
    inference(superposition,[status(thm)],[c_76405,c_83524]) ).

tcf(c_96740,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK9) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_83524]) ).

tcf(c_96741,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK10) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_83524]) ).

tcf(c_96742,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK11) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_83524]) ).

tcf(c_96743,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK13) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_83524]) ).

tcf(c_96744,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_14) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_83524]) ).

tcf(c_96745,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_15) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_83524]) ).

tcf(c_96746,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_16) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_83524]) ).

tcf(c_96747,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_17) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_83524]) ).

tcf(c_96748,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_18) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_83524]) ).

tcf(c_96749,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_83524]) ).

tcf(c_96750,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(iPr_def_13,X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_83524]) ).

tcf(c_96751,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK26(iPr_def_14)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_83524]) ).

tcf(c_96752,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_83524]) ).

tcf(c_96753,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79414,c_83524]) ).

tcf(c_96754,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79557,c_83524]) ).

tcf(c_96755,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_83524]) ).

tcf(c_96756,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79918,c_83524]) ).

tcf(c_96757,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_83504,c_83524]) ).

tcf(c_96758,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_83524]) ).

tcf(c_96759,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_83524]) ).

tcf(c_96760,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),m))),
    inference(superposition,[status(thm)],[c_80692,c_83524]) ).

tcf(c_96761,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_83524]) ).

tcf(c_96762,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_83524]) ).

tcf(c_96763,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_83524]) ).

tcf(c_96764,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_83524]) ).

tcf(c_96765,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_83524,c_65]) ).

tcf(c_96768,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)),
    inference(light_normalisation,[status(thm)],[c_96701,c_79190]) ).

tcf(c_96769,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),X1)),
    inference(light_normalisation,[status(thm)],[c_96722,c_92932]) ).

tcf(c_96770,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)),X1)),
    inference(light_normalisation,[status(thm)],[c_96721,c_92621]) ).

tcf(c_96916,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_79150,c_766]) ).

tcf(c_96918,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_255,c_766]) ).

tcf(c_96919,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_256,c_766]) ).

tcf(c_96922,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_388,c_766]) ).

tcf(c_96923,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),m)) ),
    inference(superposition,[status(thm)],[c_79190,c_766]) ).

tcf(c_96924,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59636,c_766]) ).

tcf(c_96925,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),min)) ),
    inference(superposition,[status(thm)],[c_766,c_46112]) ).

tcf(c_96926,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),d22set(min))) ),
    inference(superposition,[status(thm)],[c_766,c_1579]) ).

tcf(c_96927,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(ord_less_int,min)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_766,c_226]) ).

tcf(c_96928,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_96924,c_59638]) ).

tcf(c_96941,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0))) ),
    inference(light_normalisation,[status(thm)],[c_96922,c_79988]) ).

tcf(c_96944,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(light_normalisation,[status(thm)],[c_96919,c_92971]) ).

tcf(c_96983,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,min)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_1563,c_767]) ).

tcf(c_96985,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(superposition,[status(thm)],[c_79150,c_767]) ).

tcf(c_96987,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) ),
    inference(superposition,[status(thm)],[c_255,c_767]) ).

tcf(c_96988,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) ),
    inference(superposition,[status(thm)],[c_256,c_767]) ).

tcf(c_96991,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(superposition,[status(thm)],[c_388,c_767]) ).

tcf(c_96992,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(iPr_def_13,iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_79190,c_767]) ).

tcf(c_96993,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(iPr_def_12,one_one_int))) ),
    inference(superposition,[status(thm)],[c_59636,c_767]) ).

tcf(c_96994,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),iPr_def_14)) ),
    inference(light_normalisation,[status(thm)],[c_96993,c_59638]) ).

tcf(c_97001,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(light_normalisation,[status(thm)],[c_96991,c_79988]) ).

tcf(c_97004,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1)))) ),
    inference(light_normalisation,[status(thm)],[c_96988,c_92971]) ).

tcf(c_97014,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_79150,c_787]) ).

tcf(c_97016,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_255,c_787]) ).

tcf(c_97017,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_256,c_787]) ).

tcf(c_97020,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_388,c_787]) ).

tcf(c_97021,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),m)) ),
    inference(superposition,[status(thm)],[c_79190,c_787]) ).

tcf(c_97022,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59636,c_787]) ).

tcf(c_97023,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(ord_less_eq_int,min)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_787,c_226]) ).

tcf(c_97024,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_97022,c_59638]) ).

tcf(c_97033,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0))) ),
    inference(light_normalisation,[status(thm)],[c_97020,c_79988]) ).

tcf(c_97036,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(light_normalisation,[status(thm)],[c_97017,c_92971]) ).

tcf(c_97048,plain,
    ! [X0: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,min)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0)) ),
    inference(superposition,[status(thm)],[c_1563,c_788]) ).

tcf(c_97050,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(superposition,[status(thm)],[c_79150,c_788]) ).

tcf(c_97052,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1))))) ),
    inference(superposition,[status(thm)],[c_255,c_788]) ).

tcf(c_97053,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1)))) ),
    inference(superposition,[status(thm)],[c_256,c_788]) ).

tcf(c_97056,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(superposition,[status(thm)],[c_388,c_788]) ).

tcf(c_97057,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),m))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(iPr_def_13,iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_79190,c_788]) ).

tcf(c_97058,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(iPr_def_12,one_one_int))) ),
    inference(superposition,[status(thm)],[c_59636,c_788]) ).

tcf(c_97061,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),iPr_def_14)) ),
    inference(light_normalisation,[status(thm)],[c_97058,c_59638]) ).

tcf(c_97068,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0))) ),
    inference(light_normalisation,[status(thm)],[c_97056,c_79988]) ).

tcf(c_97071,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1)))) ),
    inference(light_normalisation,[status(thm)],[c_97053,c_92971]) ).

tcf(c_97077,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int))),
    inference(superposition,[status(thm)],[c_96004,c_226]) ).

tcf(c_97079,plain,
    ! [X0: $i] : is_int(sK27(X0,iPr_def_14)),
    inference(superposition,[status(thm)],[c_96004,c_46404]) ).

tcf(c_97081,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK27(X1,iPr_def_14)),X0)) = sK27(X1,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_46106]) ).

tcf(c_97082,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK27(X1,iPr_def_14))),X0) = pls,
    inference(superposition,[status(thm)],[c_97079,c_46104]) ).

tcf(c_97083,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK27(X0,iPr_def_14)),pls) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_880]) ).

tcf(c_97084,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK27(X0,iPr_def_14)),one_one_nat) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_608]) ).

tcf(c_97085,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK27(X0,iPr_def_14)),pls) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_524]) ).

tcf(c_97086,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),sK27(X0,iPr_def_14)) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_523]) ).

tcf(c_97087,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),sK27(X0,iPr_def_14)) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_347]) ).

tcf(c_97088,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK27(X0,iPr_def_14)),one_one_int) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_346]) ).

tcf(c_97089,plain,
    ! [X0: $i] : number_number_of_int(sK27(X0,iPr_def_14)) = sK27(X0,iPr_def_14),
    inference(superposition,[status(thm)],[c_97079,c_254]) ).

tcf(c_97123,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X0) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(iPr_def_14),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96066]) ).

tcf(c_97127,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96066]) ).

tcf(c_97139,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_95915]) ).

tcf(c_97140,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_95915]) ).

tcf(c_97143,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_95915]) ).

tcf(c_97146,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_nat_int(power_power_int(X0),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_95915]) ).

tcf(c_97153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96062]) ).

tcf(c_97154,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(iPr_def_14),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96062]) ).

tcf(c_97157,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96062]) ).

tcf(c_97161,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96062]) ).

tcf(c_97167,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96062]) ).

tcf(c_97174,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_83527,c_90800,c_91937]) ).

tcf(c_97179,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),hAPP_nat_nat(times_times_nat(X2),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_675,c_801]) ).

tcf(c_97181,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),zero_zero_real))
      | ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_495,c_801]) ).

tcf(c_97182,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),one_one_real))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_782,c_801]) ).

tcf(c_97183,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),one_one_real))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_671,c_801]) ).

tcf(c_97184,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X0),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_82839,c_801]) ).

tcf(c_97186,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(min)),one_one_real))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_85148,c_801]) ).

tcf(c_97187,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_real(power_power_real(zero_zero_real),X0) = zero_zero_real )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_801,c_1017]) ).

tcf(c_97190,plain,
    hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(min)),one_one_real)),
    inference(forward_subsumption_resolution,[status(thm)],[c_97186,c_76735]) ).

tcf(c_97199,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_674,c_803]) ).

tcf(c_97201,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),zero_zero_nat))
      | ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1063,c_803]) ).

tcf(c_97202,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1223,c_803]) ).

tcf(c_97203,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1222,c_803]) ).

tcf(c_97204,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X0),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_82316,c_803]) ).

tcf(c_97205,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_803,c_1590]) ).

tcf(c_97220,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_676,c_805]) ).

tcf(c_97221,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),pls))
      | ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_491,c_805]) ).

tcf(c_97222,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_784,c_805]) ).

tcf(c_97223,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),one_one_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_673,c_805]) ).

tcf(c_97224,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),pls))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77288,c_805]) ).

tcf(c_97225,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X0),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_82861,c_805]) ).

tcf(c_97226,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,undefined_int(int)),undefined_int(int)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77289,c_805]) ).

tcf(c_97227,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),min))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77292,c_805]) ).

tcf(c_97228,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,twoSqu1241645765sum2sq(X0)),twoSqu1241645765sum2sq(X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77295,c_805]) ).

tcf(c_97229,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),m))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77299,c_805]) ).

tcf(c_97230,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,s1),s1))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77300,c_805]) ).

tcf(c_97231,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,s),s))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77301,c_805]) ).

tcf(c_97232,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,t),t))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77302,c_805]) ).

tcf(c_97233,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK9),sK9))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77303,c_805]) ).

tcf(c_97234,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK10),sK10))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77304,c_805]) ).

tcf(c_97235,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK11),sK11))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77305,c_805]) ).

tcf(c_97236,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK13),sK13))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77306,c_805]) ).

tcf(c_97237,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14),iPr_def_14))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77311,c_805]) ).

tcf(c_97238,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_15),iPr_def_15))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77312,c_805]) ).

tcf(c_97239,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_16),iPr_def_16))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77313,c_805]) ).

tcf(c_97240,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_17),iPr_def_17))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77314,c_805]) ).

tcf(c_97241,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_18),iPr_def_18))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77315,c_805]) ).

tcf(c_97242,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),sK30(iPr_def_19)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77316,c_805]) ).

tcf(c_97243,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),one_one_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(iPr_def_11),X0))) ),
    inference(superposition,[status(thm)],[c_85131,c_805]) ).

tcf(c_97244,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_88497,c_805]) ).

tcf(c_97245,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_88516,c_805]) ).

tcf(c_97246,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_88553,c_805]) ).

tcf(c_97247,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_nat_int(power_power_int(X1),X0),hAPP_i1948725293t_bool(dvd_dvd_int,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_805,c_226]) ).

tcf(c_97248,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X1),X0),pls),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_805,c_929]) ).

tcf(c_97249,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),X0) = pls )
      | ~ is_int(hAPP_nat_int(power_power_int(pls),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_805,c_1019]) ).

tcf(c_97254,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(pls),X0) = pls )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_97249,c_67]) ).

tcf(c_97278,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(number_number_of_nat(min)),number_number_of_nat(X0)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_768,c_820]) ).

tcf(c_97279,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_820]) ).

tcf(c_97281,plain,
    ! [X0: $i] : hAPP_nat_nat(times_times_nat(zero_zero_nat),number_number_of_nat(X0)) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_97278,c_78282]) ).

tcf(c_97290,plain,
    is_int(sK30(hAPP_i1948725293t_bool(ord_less_int,iPr_def_14))),
    inference(superposition,[status(thm)],[c_1563,c_96001]) ).

tcf(c_97294,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)))),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_96088]) ).

tcf(c_97296,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X1) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96088]) ).

tcf(c_97300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),hAPP_int_int(times_times_int(X3),X3)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96088]) ).

tcf(c_97306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X3),hAPP_int_int(times_times_int(X2),X3)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_96088]) ).

tcf(c_97307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X2),X3)),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_96088]) ).

tcf(c_97310,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),number_number_of_int(hAPP_int_int(times_times_int(X2),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_96088]) ).

tcf(c_97314,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_96088]) ).

tcf(c_97315,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_96088]) ).

tcf(c_97316,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X1) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(X0),X0) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_97296,c_83223]) ).

tcf(c_97329,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_96138]) ).

tcf(c_97330,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_96138]) ).

tcf(c_97333,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_96138]) ).

tcf(c_97337,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_96138]) ).

tcf(c_97340,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X1) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96138]) ).

tcf(c_97344,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96138]) ).

tcf(c_97351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_97330,c_90904]) ).

tcf(c_97359,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))) = hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X0))),
    inference(demodulation,[status(thm)],[c_83528,c_79979,c_79918,c_92983]) ).

tcf(c_97364,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_676,c_850]) ).

tcf(c_97391,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_nat_int(power_power_int(X0),X1),hAPP_i1948725293t_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_850,c_226]) ).

tcf(c_97402,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(dvd_dvd_int,X2)))
      | hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1563,c_896]) ).

tcf(c_97403,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(X0,X1),hAPP_int_int(minus_minus_int(X0),X1))),
    inference(superposition,[status(thm)],[c_961,c_896]) ).

tcf(c_97405,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(X0,X1),min)),
    inference(superposition,[status(thm)],[c_81106,c_896]) ).

tcf(c_97406,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,hAPP_int_int(minus_minus_int(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_896]) ).

tcf(c_97407,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(number_number_of_int(X1),number_number_of_int(X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(minus_minus_int(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_879,c_896]) ).

tcf(c_97408,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(pls,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_77403,c_896]) ).

tcf(c_97409,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(pls,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_78632,c_896]) ).

tcf(c_97410,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(min,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_77407,c_896]) ).

tcf(c_97411,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(one_one_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_77402,c_896]) ).

tcf(c_97412,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(undefined_int(int),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),undefined_int(int))) ),
    inference(superposition,[status(thm)],[c_77404,c_896]) ).

tcf(c_97413,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(twoSqu1241645765sum2sq(X1),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),twoSqu1241645765sum2sq(X1))) ),
    inference(superposition,[status(thm)],[c_77410,c_896]) ).

tcf(c_97414,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(m,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),m)) ),
    inference(superposition,[status(thm)],[c_77414,c_896]) ).

tcf(c_97415,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(s1,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),s1)) ),
    inference(superposition,[status(thm)],[c_77415,c_896]) ).

tcf(c_97416,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(s,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),s)) ),
    inference(superposition,[status(thm)],[c_77416,c_896]) ).

tcf(c_97417,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(t,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),t)) ),
    inference(superposition,[status(thm)],[c_77417,c_896]) ).

tcf(c_97418,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK9,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK9)) ),
    inference(superposition,[status(thm)],[c_77418,c_896]) ).

tcf(c_97419,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK10,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK10)) ),
    inference(superposition,[status(thm)],[c_77419,c_896]) ).

tcf(c_97420,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK11,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK11)) ),
    inference(superposition,[status(thm)],[c_77420,c_896]) ).

tcf(c_97421,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK13,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK13)) ),
    inference(superposition,[status(thm)],[c_77421,c_896]) ).

tcf(c_97422,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(iPr_def_14,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_77426,c_896]) ).

tcf(c_97423,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(iPr_def_15,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_77427,c_896]) ).

tcf(c_97424,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(iPr_def_16,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_77428,c_896]) ).

tcf(c_97425,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(iPr_def_17,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_17)) ),
    inference(superposition,[status(thm)],[c_77429,c_896]) ).

tcf(c_97426,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(iPr_def_18,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_18)) ),
    inference(superposition,[status(thm)],[c_77430,c_896]) ).

tcf(c_97427,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_77431,c_896]) ).

tcf(c_97428,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X1),X1)))) ),
    inference(superposition,[status(thm)],[c_78625,c_896]) ).

tcf(c_97429,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)),number_number_of_int(X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))) ),
    inference(superposition,[status(thm)],[c_83524,c_896]) ).

tcf(c_97430,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(s),s),min),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))) ),
    inference(superposition,[status(thm)],[c_85161,c_896]) ).

tcf(c_97431,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88496,c_896]) ).

tcf(c_97432,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88515,c_896]) ).

tcf(c_97433,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_88552,c_896]) ).

tcf(c_97638,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,hAPP_int_int(minus_minus_int(X0),X1)),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1720,c_897]) ).

tcf(c_97639,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),number_number_of_int(hAPP_int_int(minus_minus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(zcong(number_number_of_int(X0),number_number_of_int(X1)),X2)) ),
    inference(superposition,[status(thm)],[c_879,c_897]) ).

tcf(c_97641,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(zcong(pls,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_78632,c_897]) ).

tcf(c_97642,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(zcong(min,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77407,c_897]) ).

tcf(c_97643,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
      | ~ hBOOL(hAPP_int_bool(zcong(one_one_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77402,c_897]) ).

tcf(c_97644,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),undefined_int(int)))
      | ~ hBOOL(hAPP_int_bool(zcong(undefined_int(int),pls),X0)) ),
    inference(superposition,[status(thm)],[c_77404,c_897]) ).

tcf(c_97645,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),twoSqu1241645765sum2sq(X0)))
      | ~ hBOOL(hAPP_int_bool(zcong(twoSqu1241645765sum2sq(X0),pls),X1)) ),
    inference(superposition,[status(thm)],[c_77410,c_897]) ).

tcf(c_97646,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),m))
      | ~ hBOOL(hAPP_int_bool(zcong(m,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77414,c_897]) ).

tcf(c_97647,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),s1))
      | ~ hBOOL(hAPP_int_bool(zcong(s1,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77415,c_897]) ).

tcf(c_97648,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),s))
      | ~ hBOOL(hAPP_int_bool(zcong(s,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77416,c_897]) ).

tcf(c_97649,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),t))
      | ~ hBOOL(hAPP_int_bool(zcong(t,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77417,c_897]) ).

tcf(c_97650,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK9))
      | ~ hBOOL(hAPP_int_bool(zcong(sK9,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77418,c_897]) ).

tcf(c_97651,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK10))
      | ~ hBOOL(hAPP_int_bool(zcong(sK10,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77419,c_897]) ).

tcf(c_97652,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK11))
      | ~ hBOOL(hAPP_int_bool(zcong(sK11,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77420,c_897]) ).

tcf(c_97653,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK13))
      | ~ hBOOL(hAPP_int_bool(zcong(sK13,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77421,c_897]) ).

tcf(c_97654,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_14))
      | ~ hBOOL(hAPP_int_bool(zcong(iPr_def_14,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77426,c_897]) ).

tcf(c_97655,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_15))
      | ~ hBOOL(hAPP_int_bool(zcong(iPr_def_15,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77427,c_897]) ).

tcf(c_97656,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_16))
      | ~ hBOOL(hAPP_int_bool(zcong(iPr_def_16,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77428,c_897]) ).

tcf(c_97657,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_17))
      | ~ hBOOL(hAPP_int_bool(zcong(iPr_def_17,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77429,c_897]) ).

tcf(c_97658,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_18))
      | ~ hBOOL(hAPP_int_bool(zcong(iPr_def_18,pls),X0)) ),
    inference(superposition,[status(thm)],[c_77430,c_897]) ).

tcf(c_97659,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),pls),X0)) ),
    inference(superposition,[status(thm)],[c_77431,c_897]) ).

tcf(c_97660,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),X1)) ),
    inference(superposition,[status(thm)],[c_78625,c_897]) ).

tcf(c_97661,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)),number_number_of_int(X1)),X2)) ),
    inference(superposition,[status(thm)],[c_83524,c_897]) ).

tcf(c_97662,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(s),s),min),X0)) ),
    inference(superposition,[status(thm)],[c_85161,c_897]) ).

tcf(c_97663,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X0)) ),
    inference(superposition,[status(thm)],[c_88496,c_897]) ).

tcf(c_97664,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X1)) ),
    inference(superposition,[status(thm)],[c_88515,c_897]) ).

tcf(c_97665,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(zcong(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)),pls),X1)) ),
    inference(superposition,[status(thm)],[c_88552,c_897]) ).

tcf(c_97666,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(hAPP_int_int(minus_minus_int(X0),X1),hAPP_i1948725293t_bool(dvd_dvd_int,X2)))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_897,c_226]) ).

tcf(c_97667,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(X0),X1),pls),X2))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_897,c_929]) ).

tcf(c_97669,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),X1) = pls )
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),X1))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),pls)) ),
    inference(superposition,[status(thm)],[c_897,c_1019]) ).

tcf(c_97775,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(X1),one_one_int)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_901]) ).

tcf(c_97776,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_78632,c_901]) ).

tcf(c_97777,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(minus_minus_int(X1),one_one_int),hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_901,c_226]) ).

tcf(c_97778,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_901,c_612]) ).

tcf(c_97779,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X1,hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_901,c_46404]) ).

tcf(c_97780,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_901,c_90699]) ).

tcf(c_97783,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK27(X1,hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_97779,c_59643]) ).

tcf(c_97786,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_97778,c_59643]) ).

tcf(c_97802,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(min,zcong(X0,X1))),
    inference(superposition,[status(thm)],[c_97405,c_226]) ).

tcf(c_97803,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(X1,X0,min))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97405,c_852]) ).

tcf(c_97811,plain,
    ! [X0: $i] : is_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_92014]) ).

tcf(c_97812,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),iPr_def_14)),X1)),
    inference(superposition,[status(thm)],[c_253,c_92014]) ).

tcf(c_97821,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_252,c_92014]) ).

tcf(c_97823,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14))),
    inference(superposition,[status(thm)],[c_79150,c_92014]) ).

tcf(c_97825,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),iPr_def_14))),X0)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_46106]) ).

tcf(c_97826,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),iPr_def_14)))),X0) = pls,
    inference(superposition,[status(thm)],[c_92014,c_46104]) ).

tcf(c_97827,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_880]) ).

tcf(c_97828,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),one_one_nat) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_608]) ).

tcf(c_97829,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_524]) ).

tcf(c_97830,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_523]) ).

tcf(c_97831,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_347]) ).

tcf(c_97832,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))),one_one_int) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_346]) ).

tcf(c_97833,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),iPr_def_14)),
    inference(superposition,[status(thm)],[c_92014,c_254]) ).

tcf(c_97869,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))))),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_93890,c_96084]) ).

tcf(c_97870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),hAPP_int_int(times_times_int(X4),X4)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96084]) ).

tcf(c_97871,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96084]) ).

tcf(c_97874,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96084]) ).

tcf(c_97878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),X2))),hAPP_int_int(times_times_int(X3),X3)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96084]) ).

tcf(c_97884,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat))),hAPP_int_int(times_times_int(X2),X2)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96084]) ).

tcf(c_97886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_int_int(times_times_int(X3),hAPP_int_int(times_times_int(X4),hAPP_int_int(times_times_int(X3),X4)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_96084]) ).

tcf(c_97887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_int_int(times_times_int(X3),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X3),X4)),X4))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_96084]) ).

tcf(c_97890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),number_number_of_int(hAPP_int_int(times_times_int(X3),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_96084]) ).

tcf(c_97894,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_96084]) ).

tcf(c_97895,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_int_int(iPr_def_13,m)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_59637,c_96084]) ).

tcf(c_97897,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(times_times_int(X0),X0) != iPr_def_18 ) ),
    inference(light_normalisation,[status(thm)],[c_97871,c_83223]) ).

tcf(c_97910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_252,c_96134]) ).

tcf(c_97911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_217,c_96134]) ).

tcf(c_97914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_382,c_96134]) ).

tcf(c_97918,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_96134]) ).

tcf(c_97920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96134]) ).

tcf(c_97921,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96134]) ).

tcf(c_97924,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96134]) ).

tcf(c_97928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96134]) ).

tcf(c_97934,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),zero_zero_nat))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96134]) ).

tcf(c_97937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_97911,c_90904]) ).

tcf(c_97947,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96169]) ).

tcf(c_97950,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),iPr_def_11))),hAPP_nat_int(power_power_int(X2),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96169]) ).

tcf(c_97952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(times_times_nat(X1),X2)))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96169]) ).

tcf(c_97954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X1)),X2))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96169]) ).

tcf(c_97958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))))),hAPP_nat_int(power_power_int(X4),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96169]) ).

tcf(c_97963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),hAPP_nat_int(power_power_int(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96169]) ).

tcf(c_97964,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96169]) ).

tcf(c_97965,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96169]) ).

tcf(c_97967,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_97964,c_78498]) ).

tcf(c_97988,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_79150,c_96174]) ).

tcf(c_97992,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X2) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96174]) ).

tcf(c_98001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96174]) ).

tcf(c_98005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(iPr_def_11),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96174]) ).

tcf(c_98008,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),hAPP_nat_int(power_power_int(X2),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96174]) ).

tcf(c_98014,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(demodulation,[status(thm)],[c_83529,c_253,c_86128,c_90801,c_90934]) ).

tcf(c_98016,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79557,c_98014]) ).

tcf(c_98017,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79437,c_98014]) ).

tcf(c_98018,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98014]) ).

tcf(c_98019,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_253,c_98014]) ).

tcf(c_98021,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1)))),
    inference(superposition,[status(thm)],[c_217,c_98014]) ).

tcf(c_98023,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_98014]) ).

tcf(c_98024,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76855,c_98014]) ).

tcf(c_98025,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_257,c_98014]) ).

tcf(c_98027,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(one_one_int),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_76874,c_98014]) ).

tcf(c_98028,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),m)))),
    inference(superposition,[status(thm)],[c_256,c_98014]) ).

tcf(c_98030,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m)),X0))),
    inference(superposition,[status(thm)],[c_93890,c_98014]) ).

tcf(c_98031,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),X1))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X0))),
    inference(superposition,[status(thm)],[c_78930,c_98014]) ).

tcf(c_98032,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))),
    inference(superposition,[status(thm)],[c_78938,c_98014]) ).

tcf(c_98034,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X1))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),X0))),
    inference(superposition,[status(thm)],[c_79161,c_98014]) ).

tcf(c_98035,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X1),iPr_def_14))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79901,c_98014]) ).

tcf(c_98036,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79904,c_98014]) ).

tcf(c_98037,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_83616,c_98014]) ).

tcf(c_98038,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_85658,c_98014]) ).

tcf(c_98039,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88494,c_98014]) ).

tcf(c_98040,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88513,c_98014]) ).

tcf(c_98041,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88550,c_98014]) ).

tcf(c_98042,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_92656,c_98014]) ).

tcf(c_98043,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X1)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X0))),
    inference(superposition,[status(thm)],[c_92625,c_98014]) ).

tcf(c_98044,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_92936,c_98014]) ).

tcf(c_98045,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93551,c_98014]) ).

tcf(c_98046,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93822,c_98014]) ).

tcf(c_98047,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_94573,c_98014]) ).

tcf(c_98048,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_94594,c_98014]) ).

tcf(c_98049,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_94672,c_98014]) ).

tcf(c_98050,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_94695,c_98014]) ).

tcf(c_98051,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95015,c_98014]) ).

tcf(c_98052,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95041,c_98014]) ).

tcf(c_98053,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95257,c_98014]) ).

tcf(c_98054,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95286,c_98014]) ).

tcf(c_98055,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95382,c_98014]) ).

tcf(c_98056,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95414,c_98014]) ).

tcf(c_98058,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98014]) ).

tcf(c_98059,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_253,c_98014]) ).

tcf(c_98061,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_252,c_98014]) ).

tcf(c_98062,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_257,c_98014]) ).

tcf(c_98064,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))),X2))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_255,c_98014]) ).

tcf(c_98065,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),pls)),X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m))),
    inference(superposition,[status(thm)],[c_77148,c_98014]) ).

tcf(c_98066,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_98014]) ).

tcf(c_98067,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),one_one_int)),X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_59636,c_98014]) ).

tcf(c_98069,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98014,c_93890]) ).

tcf(c_98070,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))))),
    inference(superposition,[status(thm)],[c_98014,c_1042]) ).

tcf(c_98071,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))) = pls,
    inference(superposition,[status(thm)],[c_98014,c_92002]) ).

tcf(c_98072,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))),X2)),
    inference(superposition,[status(thm)],[c_98014,c_252]) ).

tcf(c_98073,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_int_int(times_times_int(X2),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_833]) ).

tcf(c_98074,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_98014,c_76863]) ).

tcf(c_98075,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_98014,c_76535]) ).

tcf(c_98076,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))))),
    inference(superposition,[status(thm)],[c_98014,c_76498]) ).

tcf(c_98077,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_98014,c_1045]) ).

tcf(c_98078,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_98014,c_217]) ).

tcf(c_98080,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X1),m))))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98014,c_833]) ).

tcf(c_98081,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88519]) ).

tcf(c_98082,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88518]) ).

tcf(c_98083,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88516]) ).

tcf(c_98084,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88515]) ).

tcf(c_98085,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88521]) ).

tcf(c_98086,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_88319]) ).

tcf(c_98087,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),pls),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_84092]) ).

tcf(c_98088,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),pls))),
    inference(superposition,[status(thm)],[c_98014,c_84084]) ).

tcf(c_98089,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))) = pls,
    inference(superposition,[status(thm)],[c_98014,c_83484]) ).

tcf(c_98090,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_79573]) ).

tcf(c_98091,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_79414]) ).

tcf(c_98092,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_98014,c_78432]) ).

tcf(c_98093,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))),
    inference(superposition,[status(thm)],[c_98014,c_78420]) ).

tcf(c_98094,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_78405]) ).

tcf(c_98095,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_78397]) ).

tcf(c_98097,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_90930]) ).

tcf(c_98098,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88513]) ).

tcf(c_98099,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_98014,c_88514]) ).

tcf(c_98102,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98014,c_93890]) ).

tcf(c_98103,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))))),
    inference(superposition,[status(thm)],[c_98014,c_1042]) ).

tcf(c_98104,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))) = pls,
    inference(superposition,[status(thm)],[c_98014,c_92002]) ).

tcf(c_98105,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),X2)),
    inference(superposition,[status(thm)],[c_98014,c_252]) ).

tcf(c_98106,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_int_int(times_times_int(X2),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_833]) ).

tcf(c_98107,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))
      | ~ is_int(sK30(iPr_def_19)) ),
    inference(superposition,[status(thm)],[c_98014,c_76863]) ).

tcf(c_98108,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_98014,c_76535]) ).

tcf(c_98109,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))))),
    inference(superposition,[status(thm)],[c_98014,c_76498]) ).

tcf(c_98110,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_98014,c_1045]) ).

tcf(c_98111,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1)))),
    inference(superposition,[status(thm)],[c_98014,c_217]) ).

tcf(c_98113,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1)))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_98014,c_833]) ).

tcf(c_98114,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88519]) ).

tcf(c_98115,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88518]) ).

tcf(c_98116,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))),one_one_nat) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88516]) ).

tcf(c_98117,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))),pls) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88515]) ).

tcf(c_98118,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88521]) ).

tcf(c_98119,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_88319]) ).

tcf(c_98120,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),pls),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_84092]) ).

tcf(c_98121,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))),pls))),
    inference(superposition,[status(thm)],[c_98014,c_84084]) ).

tcf(c_98122,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))) = pls,
    inference(superposition,[status(thm)],[c_98014,c_83484]) ).

tcf(c_98123,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_79573]) ).

tcf(c_98124,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_79414]) ).

tcf(c_98125,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_98014,c_78432]) ).

tcf(c_98126,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(sK30(iPr_def_19),zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))),
    inference(superposition,[status(thm)],[c_98014,c_78420]) ).

tcf(c_98127,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_78405]) ).

tcf(c_98128,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK30(iPr_def_19),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_78397]) ).

tcf(c_98130,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(sK14(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_98014,c_90930]) ).

tcf(c_98131,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),sK30(iPr_def_19),sK30(iPr_def_19))),X0)) = sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),sK30(iPr_def_19),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98014,c_88513]) ).

tcf(c_98132,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),sK30(iPr_def_19),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_98014,c_88514]) ).

tcf(c_98133,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),hAPP_int_int(plus_plus_int(X1),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98014,c_98014]) ).

tcf(c_98134,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_98107,c_76385]) ).

tcf(c_98135,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_98074,c_76385]) ).

tcf(c_98136,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls),
    inference(light_normalisation,[status(thm)],[c_98023,c_574]) ).

tcf(c_98137,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),pls)),X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_98065,c_76855,c_77366]) ).

tcf(c_98138,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(light_normalisation,[status(thm)],[c_98027,c_59636]) ).

tcf(c_98139,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(light_normalisation,[status(thm)],[c_98024,c_59637]) ).

tcf(c_98140,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98037,c_79573]) ).

tcf(c_98141,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(light_normalisation,[status(thm)],[c_98017,c_79918]) ).

tcf(c_98142,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(light_normalisation,[status(thm)],[c_98016,c_79918]) ).

tcf(c_98143,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98042,c_79573]) ).

tcf(c_98144,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98045,c_79573]) ).

tcf(c_98145,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98046,c_79573]) ).

tcf(c_98146,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98048,c_79573]) ).

tcf(c_98147,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98050,c_79573]) ).

tcf(c_98148,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98047,c_79573]) ).

tcf(c_98149,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98052,c_79573]) ).

tcf(c_98150,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98049,c_79573]) ).

tcf(c_98151,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98054,c_79573]) ).

tcf(c_98152,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98051,c_79573]) ).

tcf(c_98153,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98056,c_79573]) ).

tcf(c_98154,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98053,c_79573]) ).

tcf(c_98155,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_98055,c_79573]) ).

tcf(c_98156,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_98039,c_88957]) ).

tcf(c_98509,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(minus_minus_real(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1241,c_955]) ).

tcf(c_98511,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),X1))),zero_zero_real)) ),
    inference(superposition,[status(thm)],[c_878,c_955]) ).

tcf(c_98521,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),X1))),zero_zero_real))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),number267125858f_real(X1))) ),
    inference(superposition,[status(thm)],[c_878,c_956]) ).

tcf(c_98540,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),number267125858f_real(X1)))
      | ( number267125858f_real(X0) = number267125858f_real(X1) ) ),
    inference(superposition,[status(thm)],[c_957,c_138]) ).

tcf(c_98542,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_957,c_970]) ).

tcf(c_98550,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X0)))
      | ( number267125858f_real(X0) = number267125858f_real(X1) ) ),
    inference(superposition,[status(thm)],[c_957,c_138]) ).

tcf(c_98551,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,number_number_of_int(X0)))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),one_one_real))
      | ( number267125858f_real(X0) = one_one_real ) ),
    inference(superposition,[status(thm)],[c_957,c_89246]) ).

tcf(c_98552,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X0))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_957,c_970]) ).

tcf(c_98553,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),zero_zero_real))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X0),X0)))
      | ( hAPP_real_real(plus_plus_real(X0),X0) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_957,c_551]) ).

tcf(c_98554,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1))))
      | ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),X1)) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_957,c_596]) ).

tcf(c_98555,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ( number267125858f_real(X0) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_957,c_625]) ).

tcf(c_98557,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),X0)))
      | ( hAPP_real_real(times_times_real(X0),X0) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_957,c_1201]) ).

tcf(c_98559,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),iPr_def_11)))
      | ( hAPP_nat_real(power_power_real(X0),iPr_def_11) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_957,c_81997]) ).

tcf(c_98612,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X0),iPr_def_11)),X1),
    inference(superposition,[status(thm)],[c_82839,c_975]) ).

tcf(c_98615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_219,c_975]) ).

tcf(c_98617,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X2)),
    inference(superposition,[status(thm)],[c_976,c_975]) ).

tcf(c_98620,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0))),X2) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),hAPP_real_real(times_times_real(X0),X2)),
    inference(superposition,[status(thm)],[c_370,c_975]) ).

tcf(c_98621,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X0)),X1),
    inference(superposition,[status(thm)],[c_373,c_975]) ).

tcf(c_98623,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),hAPP_real_real(times_times_real(number267125858f_real(X0)),X1)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),X1),
    inference(superposition,[status(thm)],[c_408,c_975]) ).

tcf(c_98624,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(zero_zero_real),hAPP_real_real(times_times_real(X0),X1)) = hAPP_real_real(times_times_real(zero_zero_real),X1),
    inference(superposition,[status(thm)],[c_1002,c_975]) ).

tcf(c_98625,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(zero_zero_real),X1)) = hAPP_real_real(times_times_real(zero_zero_real),X1),
    inference(superposition,[status(thm)],[c_999,c_975]) ).

tcf(c_98626,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X1)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X0),X0)),X1),
    inference(superposition,[status(thm)],[c_14792,c_975]) ).

tcf(c_98627,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1)))),hAPP_real_real(times_times_real(X2),X2))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_975,c_596]) ).

tcf(c_98628,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1)))),hAPP_real_real(times_times_real(X2),X2)))),
    inference(superposition,[status(thm)],[c_975,c_585]) ).

tcf(c_98629,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_975,c_82839]) ).

tcf(c_98630,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1)))))
      | ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_975,c_759]) ).

tcf(c_98631,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1)))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_975,c_1201]) ).

tcf(c_98632,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X0),X1))))),
    inference(superposition,[status(thm)],[c_975,c_1134]) ).

tcf(c_98633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X3)),
    inference(superposition,[status(thm)],[c_975,c_975]) ).

tcf(c_98635,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)))),
    inference(superposition,[status(thm)],[c_975,c_1043]) ).

tcf(c_98636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),hAPP_real_real(times_times_real(X2),X3)) = hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X3))),
    inference(superposition,[status(thm)],[c_975,c_219]) ).

tcf(c_98638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X1),X2)),X3)) = hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X0),X3))),
    inference(superposition,[status(thm)],[c_975,c_219]) ).

tcf(c_98640,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),X0))) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X1),X2)),one_one_real)),X0),
    inference(superposition,[status(thm)],[c_975,c_370]) ).

tcf(c_98642,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),X0)))),
    inference(superposition,[status(thm)],[c_975,c_1040]) ).

tcf(c_98643,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),one_one_real)) = hAPP_real_real(times_times_real(X0),X1),
    inference(superposition,[status(thm)],[c_975,c_325]) ).

tcf(c_98644,plain,
    ! [X0: $i,X1: $i] : hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),zero_zero_real)) = zero_zero_real,
    inference(superposition,[status(thm)],[c_975,c_999]) ).

tcf(c_98645,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X1),X2))))),zero_zero_real)),
    inference(superposition,[status(thm)],[c_975,c_596]) ).

tcf(c_98646,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X0),X0)),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X1),X2)))))),
    inference(superposition,[status(thm)],[c_975,c_585]) ).

tcf(c_98650,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),one_one_real))),X2) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X1),one_one_real)),hAPP_real_real(times_times_real(X0),X2)),
    inference(light_normalisation,[status(thm)],[c_98620,c_94193]) ).

tcf(c_98745,plain,
    hBOOL(member_int(m,zcong(pls,m))),
    inference(superposition,[status(thm)],[c_76934,c_93296]) ).

tcf(c_98749,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))),
    inference(demodulation,[status(thm)],[c_94380,c_253]) ).

tcf(c_98750,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_59638,c_98749]) ).

tcf(c_98751,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_59639,c_98749]) ).

tcf(c_98752,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_59640,c_98749]) ).

tcf(c_98753,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_59642,c_98749]) ).

tcf(c_98754,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),min)),
    inference(superposition,[status(thm)],[c_76610,c_98749]) ).

tcf(c_98755,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)),
    inference(superposition,[status(thm)],[c_77245,c_98749]) ).

tcf(c_98756,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
    inference(superposition,[status(thm)],[c_82935,c_98749]) ).

tcf(c_98758,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X1))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X1)),
    inference(superposition,[status(thm)],[c_98749,c_46106]) ).

tcf(c_98759,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_98749,c_46104]) ).

tcf(c_98760,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_880]) ).

tcf(c_98761,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_608]) ).

tcf(c_98762,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_524]) ).

tcf(c_98763,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_523]) ).

tcf(c_98764,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_347]) ).

tcf(c_98765,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_346]) ).

tcf(c_98766,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)),
    inference(superposition,[status(thm)],[c_98749,c_254]) ).

tcf(c_98789,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),
    inference(demodulation,[status(thm)],[c_98751,c_253]) ).

tcf(c_98790,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_46106]) ).

tcf(c_98791,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_98789,c_46104]) ).

tcf(c_98792,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_880]) ).

tcf(c_98793,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_608]) ).

tcf(c_98794,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_524]) ).

tcf(c_98795,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_523]) ).

tcf(c_98796,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_347]) ).

tcf(c_98797,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_346]) ).

tcf(c_98798,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98789,c_254]) ).

tcf(c_98811,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),
    inference(demodulation,[status(thm)],[c_98752,c_253]) ).

tcf(c_98812,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_46106]) ).

tcf(c_98813,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_98811,c_46104]) ).

tcf(c_98814,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_880]) ).

tcf(c_98815,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_608]) ).

tcf(c_98816,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_524]) ).

tcf(c_98817,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_523]) ).

tcf(c_98818,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_347]) ).

tcf(c_98819,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_346]) ).

tcf(c_98820,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_98811,c_254]) ).

tcf(c_98870,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))),
    inference(superposition,[status(thm)],[c_79557,c_98134]) ).

tcf(c_98871,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_98134]) ).

tcf(c_98872,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98134]) ).

tcf(c_98873,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),
    inference(superposition,[status(thm)],[c_253,c_98134]) ).

tcf(c_98875,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),
    inference(superposition,[status(thm)],[c_217,c_98134]) ).

tcf(c_98877,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls))),
    inference(superposition,[status(thm)],[c_1001,c_98134]) ).

tcf(c_98878,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))))),
    inference(superposition,[status(thm)],[c_76855,c_98134]) ).

tcf(c_98879,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))),
    inference(superposition,[status(thm)],[c_257,c_98134]) ).

tcf(c_98881,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))),
    inference(superposition,[status(thm)],[c_76874,c_98134]) ).

tcf(c_98882,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))),
    inference(superposition,[status(thm)],[c_256,c_98134]) ).

tcf(c_98884,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1)))),
    inference(superposition,[status(thm)],[c_93890,c_98134]) ).

tcf(c_98885,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1)))),
    inference(superposition,[status(thm)],[c_78930,c_98134]) ).

tcf(c_98886,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0)))),
    inference(superposition,[status(thm)],[c_78938,c_98134]) ).

tcf(c_98887,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)))),
    inference(superposition,[status(thm)],[c_79190,c_98134]) ).

tcf(c_98888,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1)))),
    inference(superposition,[status(thm)],[c_79161,c_98134]) ).

tcf(c_98889,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1)))),
    inference(superposition,[status(thm)],[c_79901,c_98134]) ).

tcf(c_98890,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0)))),
    inference(superposition,[status(thm)],[c_79904,c_98134]) ).

tcf(c_98892,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),
    inference(superposition,[status(thm)],[c_85658,c_98134]) ).

tcf(c_98893,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)))),
    inference(superposition,[status(thm)],[c_88494,c_98134]) ).

tcf(c_98894,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_88513,c_98134]) ).

tcf(c_98895,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_88550,c_98134]) ).

tcf(c_98897,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))),
    inference(superposition,[status(thm)],[c_92625,c_98134]) ).

tcf(c_98898,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_92936,c_98134]) ).

tcf(c_98899,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),
    inference(superposition,[status(thm)],[c_93551,c_98134]) ).

tcf(c_98911,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),
    inference(superposition,[status(thm)],[c_98134,c_46106]) ).

tcf(c_98912,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98134,c_46104]) ).

tcf(c_98913,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_880]) ).

tcf(c_98914,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_608]) ).

tcf(c_98915,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_524]) ).

tcf(c_98916,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_523]) ).

tcf(c_98917,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_347]) ).

tcf(c_98918,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_346]) ).

tcf(c_98919,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_98134,c_254]) ).

tcf(c_98920,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),
    inference(light_normalisation,[status(thm)],[c_98877,c_574]) ).

tcf(c_98924,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),X1)))),
    inference(light_normalisation,[status(thm)],[c_98884,c_93903]) ).

tcf(c_98925,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_98893,c_88957]) ).

tcf(c_98926,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),
    inference(light_normalisation,[status(thm)],[c_98895,c_89816]) ).

tcf(c_98927,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),
    inference(light_normalisation,[status(thm)],[c_98894,c_89611]) ).

tcf(c_99023,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79573,c_98135]) ).

tcf(c_99024,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_79414,c_98135]) ).

tcf(c_99025,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98135]) ).

tcf(c_99028,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),
    inference(superposition,[status(thm)],[c_252,c_98135]) ).

tcf(c_99030,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_59637,c_98135]) ).

tcf(c_99033,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),
    inference(superposition,[status(thm)],[c_255,c_98135]) ).

tcf(c_99034,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m)))),
    inference(superposition,[status(thm)],[c_77148,c_98135]) ).

tcf(c_99035,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))))),
    inference(superposition,[status(thm)],[c_79190,c_98135]) ).

tcf(c_99036,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))),
    inference(superposition,[status(thm)],[c_59636,c_98135]) ).

tcf(c_99037,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),
    inference(superposition,[status(thm)],[c_98135,c_46106]) ).

tcf(c_99038,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98135,c_46104]) ).

tcf(c_99039,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_880]) ).

tcf(c_99040,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_608]) ).

tcf(c_99041,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_524]) ).

tcf(c_99042,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_523]) ).

tcf(c_99043,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_347]) ).

tcf(c_99044,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_346]) ).

tcf(c_99045,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_98135,c_254]) ).

tcf(c_99046,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),
    inference(light_normalisation,[status(thm)],[c_99034,c_76855,c_77366]) ).

tcf(c_99103,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(demodulation,[status(thm)],[c_98878,c_77366,c_90827]) ).

tcf(c_99104,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_12,m))))),
    inference(superposition,[status(thm)],[c_79557,c_98881]) ).

tcf(c_99105,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(iPr_def_12,m))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_98881]) ).

tcf(c_99106,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_12,m)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98881]) ).

tcf(c_99109,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X1))))),
    inference(superposition,[status(thm)],[c_217,c_98881]) ).

tcf(c_99112,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,m))))),
    inference(superposition,[status(thm)],[c_76855,c_98881]) ).

tcf(c_99113,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X1))),
    inference(superposition,[status(thm)],[c_98881,c_46106]) ).

tcf(c_99114,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98881,c_46104]) ).

tcf(c_99115,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_880]) ).

tcf(c_99116,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_608]) ).

tcf(c_99117,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_524]) ).

tcf(c_99118,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_523]) ).

tcf(c_99119,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_347]) ).

tcf(c_99120,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_346]) ).

tcf(c_99121,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_98881,c_254]) ).

tcf(c_99122,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),one_one_int)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_99105,c_83540]) ).

tcf(c_99134,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(demodulation,[status(thm)],[c_98886,c_79415,c_90827,c_90801,c_91959]) ).

tcf(c_99135,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))),
    inference(demodulation,[status(thm)],[c_98887,c_79415,c_79460,c_90827,c_90801,c_91959]) ).

tcf(c_99136,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(demodulation,[status(thm)],[c_99030,c_77366,c_90827]) ).

tcf(c_99137,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),
    inference(demodulation,[status(thm)],[c_99035,c_79438,c_79457,c_90827,c_90801]) ).

tcf(c_99140,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_93551,c_83532]) ).

tcf(c_99141,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_93822,c_83532]) ).

tcf(c_99142,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_94573,c_83532]) ).

tcf(c_99143,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_94594,c_83532]) ).

tcf(c_99144,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_94672,c_83532]) ).

tcf(c_99145,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_94695,c_83532]) ).

tcf(c_99146,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95015,c_83532]) ).

tcf(c_99147,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95041,c_83532]) ).

tcf(c_99148,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95257,c_83532]) ).

tcf(c_99149,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95286,c_83532]) ).

tcf(c_99150,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95382,c_83532]) ).

tcf(c_99151,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95414,c_83532]) ).

tcf(c_99152,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),pls)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),pls)),X0)),
    inference(superposition,[status(thm)],[c_574,c_83532]) ).

tcf(c_99153,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),min)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),min)),X0)),
    inference(superposition,[status(thm)],[c_76397,c_83532]) ).

tcf(c_99154,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),one_one_int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),one_one_int)),X0)),
    inference(superposition,[status(thm)],[c_76393,c_83532]) ).

tcf(c_99155,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),undefined_int(int))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),undefined_int(int))),X0)),
    inference(superposition,[status(thm)],[c_76395,c_83532]) ).

tcf(c_99156,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))),X1)),
    inference(superposition,[status(thm)],[c_76399,c_83532]) ).

tcf(c_99157,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))),X2)),
    inference(superposition,[status(thm)],[c_76401,c_83532]) ).

tcf(c_99158,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),m)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),m)),X0)),
    inference(superposition,[status(thm)],[c_76402,c_83532]) ).

tcf(c_99159,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),s1)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),s1)),X0)),
    inference(superposition,[status(thm)],[c_76403,c_83532]) ).

tcf(c_99160,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),s)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),s)),X0)),
    inference(superposition,[status(thm)],[c_76404,c_83532]) ).

tcf(c_99161,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),t)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),t)),X0)),
    inference(superposition,[status(thm)],[c_76405,c_83532]) ).

tcf(c_99162,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK9)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK9)),X0)),
    inference(superposition,[status(thm)],[c_76406,c_83532]) ).

tcf(c_99163,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK10)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK10)),X0)),
    inference(superposition,[status(thm)],[c_76407,c_83532]) ).

tcf(c_99164,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK11)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK11)),X0)),
    inference(superposition,[status(thm)],[c_76408,c_83532]) ).

tcf(c_99165,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK13)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK13)),X0)),
    inference(superposition,[status(thm)],[c_76409,c_83532]) ).

tcf(c_99166,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_14)),X0)),
    inference(superposition,[status(thm)],[c_76410,c_83532]) ).

tcf(c_99167,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_15)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_15)),X0)),
    inference(superposition,[status(thm)],[c_76411,c_83532]) ).

tcf(c_99168,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_16)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_16)),X0)),
    inference(superposition,[status(thm)],[c_76412,c_83532]) ).

tcf(c_99169,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_17)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_17)),X0)),
    inference(superposition,[status(thm)],[c_76413,c_83532]) ).

tcf(c_99170,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_18)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),iPr_def_18)),X0)),
    inference(superposition,[status(thm)],[c_76414,c_83532]) ).

tcf(c_99171,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_76415,c_83532]) ).

tcf(c_99172,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),X1)),
    inference(superposition,[status(thm)],[c_77366,c_83532]) ).

tcf(c_99173,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),X0)),
    inference(superposition,[status(thm)],[c_78203,c_83532]) ).

tcf(c_99174,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_79573,c_83532]) ).

tcf(c_99175,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_79414,c_83532]) ).

tcf(c_99176,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79557,c_83532]) ).

tcf(c_99177,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_79437,c_83532]) ).

tcf(c_99178,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X0))),X1)),
    inference(superposition,[status(thm)],[c_79918,c_83532]) ).

tcf(c_99179,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),m))),X1)),
    inference(superposition,[status(thm)],[c_83504,c_83532]) ).

tcf(c_99180,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X0))),X1)),
    inference(superposition,[status(thm)],[c_80664,c_83532]) ).

tcf(c_99181,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))),X1)),
    inference(superposition,[status(thm)],[c_80677,c_83532]) ).

tcf(c_99182,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),m))),X1)),
    inference(superposition,[status(thm)],[c_80692,c_83532]) ).

tcf(c_99183,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_80705,c_83532]) ).

tcf(c_99184,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X0)),
    inference(superposition,[status(thm)],[c_88502,c_83532]) ).

tcf(c_99185,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_88521,c_83532]) ).

tcf(c_99186,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_88558,c_83532]) ).

tcf(c_99187,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),pls) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),pls)),
    inference(superposition,[status(thm)],[c_574,c_83532]) ).

tcf(c_99188,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),min) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),min)),
    inference(superposition,[status(thm)],[c_76397,c_83532]) ).

tcf(c_99189,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),one_one_int) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_83532]) ).

tcf(c_99190,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),undefined_int(int)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_83532]) ).

tcf(c_99191,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),twoSqu1241645765sum2sq(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_83532]) ).

tcf(c_99192,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(X1,X2)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_83532]) ).

tcf(c_99193,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),m) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),m)),
    inference(superposition,[status(thm)],[c_76402,c_83532]) ).

tcf(c_99194,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),s1) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),s1)),
    inference(superposition,[status(thm)],[c_76403,c_83532]) ).

tcf(c_99195,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),s) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),s)),
    inference(superposition,[status(thm)],[c_76404,c_83532]) ).

tcf(c_99196,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),t) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),t)),
    inference(superposition,[status(thm)],[c_76405,c_83532]) ).

tcf(c_99197,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK9) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_83532]) ).

tcf(c_99198,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK10) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_83532]) ).

tcf(c_99199,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK11) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_83532]) ).

tcf(c_99200,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK13) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_83532]) ).

tcf(c_99201,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_14) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_83532]) ).

tcf(c_99202,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_15) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_83532]) ).

tcf(c_99203,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_16) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_83532]) ).

tcf(c_99204,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_17) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_83532]) ).

tcf(c_99205,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),iPr_def_18) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_83532]) ).

tcf(c_99206,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_83532]) ).

tcf(c_99207,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(iPr_def_13,X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_83532]) ).

tcf(c_99208,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK26(iPr_def_14)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_83532]) ).

tcf(c_99209,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_79573,c_83532]) ).

tcf(c_99211,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79557,c_83532]) ).

tcf(c_99212,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_83532]) ).

tcf(c_99213,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79918,c_83532]) ).

tcf(c_99214,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),m))),
    inference(superposition,[status(thm)],[c_83504,c_83532]) ).

tcf(c_99215,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_83532]) ).

tcf(c_99216,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_80677,c_83532]) ).

tcf(c_99217,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),m))),
    inference(superposition,[status(thm)],[c_80692,c_83532]) ).

tcf(c_99218,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_83532]) ).

tcf(c_99219,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_83532]) ).

tcf(c_99220,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_83532]) ).

tcf(c_99221,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_83532]) ).

tcf(c_99222,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_83532,c_65]) ).

tcf(c_99223,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_83532,c_93890]) ).

tcf(c_99225,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_83532,c_1042]) ).

tcf(c_99226,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) = pls,
    inference(superposition,[status(thm)],[c_83532,c_92002]) ).

tcf(c_99227,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),X2)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2),
    inference(superposition,[status(thm)],[c_83532,c_252]) ).

tcf(c_99228,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),hAPP_int_int(times_times_int(X2),number_number_of_int(X1))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_83532,c_833]) ).

tcf(c_99229,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))
      | ~ is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_83532,c_76863]) ).

tcf(c_99230,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)),
    inference(superposition,[status(thm)],[c_83532,c_253]) ).

tcf(c_99231,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_83532,c_76535]) ).

tcf(c_99232,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_83532,c_76498]) ).

tcf(c_99233,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_83532,c_1045]) ).

tcf(c_99234,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(X1),number_number_of_int(X2))) = hAPP_int_int(times_times_int(X1),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X2))),
    inference(superposition,[status(thm)],[c_83532,c_217]) ).

tcf(c_99236,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(X1)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_83532,c_833]) ).

tcf(c_99237,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_83532,c_98134]) ).

tcf(c_99238,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(number_number_of_int(X1)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_83532,c_98014]) ).

tcf(c_99243,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)),
    inference(light_normalisation,[status(thm)],[c_99158,c_79190]) ).

tcf(c_99244,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),X1)),
    inference(light_normalisation,[status(thm)],[c_99179,c_92932]) ).

tcf(c_99245,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)),X1)),
    inference(light_normalisation,[status(thm)],[c_99178,c_92621]) ).

tcf(c_99520,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_nat_real(power_power_real(X0),iPr_def_11) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_82839,c_995]) ).

tcf(c_99522,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_975,c_995]) ).

tcf(c_99523,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),X2) = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_219,c_995]) ).

tcf(c_99528,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X1),one_one_real) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_370,c_995]) ).

tcf(c_99530,plain,
    ! [X0: $i,X1: $i] :
      ( ( number267125858f_real(X1) = zero_zero_real )
      | ( number267125858f_real(X0) = zero_zero_real )
      | ( number267125858f_real(hAPP_int_int(times_times_int(X0),X1)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_383,c_995]) ).

tcf(c_99531,plain,
    ! [X0: $i] :
      ( ( number267125858f_real(X0) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = zero_zero_real )
      | ( number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0)) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_408,c_995]) ).

tcf(c_99534,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X0),X0) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_14792,c_995]) ).

tcf(c_99546,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = zero_zero_real )
      | ( hAPP_real_real(plus_plus_real(X1),one_one_real) = zero_zero_real )
      | ( hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),one_one_real)) != zero_zero_real ) ),
    inference(light_normalisation,[status(thm)],[c_99528,c_94193]) ).

tcf(c_99572,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X2),X1)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_801,c_1022]) ).

tcf(c_99575,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X1),X0)),X2))),
    inference(superposition,[status(thm)],[c_1043,c_1022]) ).

tcf(c_99577,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X0),iPr_def_11)),X1)) ),
    inference(superposition,[status(thm)],[c_82839,c_1022]) ).

tcf(c_99579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X2),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_975,c_1022]) ).

tcf(c_99580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X2)),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_219,c_1022]) ).

tcf(c_99583,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_325,c_1022]) ).

tcf(c_99585,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0))),X2)) ),
    inference(superposition,[status(thm)],[c_370,c_1022]) ).

tcf(c_99586,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_373,c_1022]) ).

tcf(c_99587,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X1)),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(hAPP_int_int(times_times_int(X0),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_383,c_1022]) ).

tcf(c_99588,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X0)),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),X1)) ),
    inference(superposition,[status(thm)],[c_408,c_1022]) ).

tcf(c_99589,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X0))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_1002,c_1022]) ).

tcf(c_99591,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_14792,c_1022]) ).

tcf(c_99604,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),one_one_real))),X2)) ),
    inference(light_normalisation,[status(thm)],[c_99585,c_94193]) ).

tcf(c_99630,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_803,c_1023]) ).

tcf(c_99633,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),X0)),X2))),
    inference(superposition,[status(thm)],[c_1044,c_1023]) ).

tcf(c_99634,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0)))),
    inference(superposition,[status(thm)],[c_1041,c_1023]) ).

tcf(c_99635,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),sK35(X2,hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1577,c_1023]) ).

tcf(c_99636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),hAPP_nat_nat(div_mod_nat(X0),X3)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X2)),X3) ),
    inference(superposition,[status(thm)],[c_1711,c_1023]) ).

tcf(c_99637,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),X1)) ),
    inference(superposition,[status(thm)],[c_82316,c_1023]) ).

tcf(c_99639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_218,c_1023]) ).

tcf(c_99642,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1413,c_1023]) ).

tcf(c_99644,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1336,c_1023]) ).

tcf(c_99680,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X2))
      | is_int(sK30(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)))) ),
    inference(superposition,[status(thm)],[c_1563,c_1024]) ).

tcf(c_99681,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X2),X1)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_805,c_1024]) ).

tcf(c_99682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),hAPP_int_int(minus_minus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),hAPP_int_int(times_times_int(X2),X3))) ),
    inference(superposition,[status(thm)],[c_897,c_1024]) ).

tcf(c_99685,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X0)),X2))),
    inference(superposition,[status(thm)],[c_1045,c_1024]) ).

tcf(c_99687,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X1),X0)))),
    inference(superposition,[status(thm)],[c_76497,c_1024]) ).

tcf(c_99688,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1720,c_1024]) ).

tcf(c_99689,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X0),iPr_def_11)),X1)) ),
    inference(superposition,[status(thm)],[c_82861,c_1024]) ).

tcf(c_99692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_252,c_1024]) ).

tcf(c_99693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X2)),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_217,c_1024]) ).

tcf(c_99695,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1004,c_1024]) ).

tcf(c_99696,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X1)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_382,c_1024]) ).

tcf(c_99699,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,m),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(iPr_def_13,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_76855,c_1024]) ).

tcf(c_99707,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79150,c_1024]) ).

tcf(c_99708,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X1)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_83532,c_1024]) ).

tcf(c_99712,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0)))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)) ),
    inference(superposition,[status(thm)],[c_96186,c_1024]) ).

tcf(c_99713,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) ),
    inference(superposition,[status(thm)],[c_98014,c_1024]) ).

tcf(c_99714,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) ),
    inference(superposition,[status(thm)],[c_98014,c_1024]) ).

tcf(c_99715,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(iPr_def_13,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_59637,c_1024]) ).

tcf(c_99786,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),
    inference(demodulation,[status(thm)],[c_98753,c_253]) ).

tcf(c_99787,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_46106]) ).

tcf(c_99788,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_99786,c_46104]) ).

tcf(c_99789,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_880]) ).

tcf(c_99790,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_608]) ).

tcf(c_99791,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_524]) ).

tcf(c_99792,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_523]) ).

tcf(c_99793,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_347]) ).

tcf(c_99794,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_346]) ).

tcf(c_99795,plain,
    number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99786,c_254]) ).

tcf(c_99798,plain,
    is_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),
    inference(demodulation,[status(thm)],[c_98754,c_253]) ).

tcf(c_99799,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_46106]) ).

tcf(c_99800,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_99798,c_46104]) ).

tcf(c_99801,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_880]) ).

tcf(c_99802,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),one_one_nat) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_608]) ).

tcf(c_99803,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),pls) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_524]) ).

tcf(c_99804,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_523]) ).

tcf(c_99805,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(min),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_347]) ).

tcf(c_99806,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))),one_one_int) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_346]) ).

tcf(c_99807,plain,
    number_number_of_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(min),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_99798,c_254]) ).

tcf(c_99863,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_99036]) ).

tcf(c_99869,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_12,m)))))),
    inference(superposition,[status(thm)],[c_252,c_99036]) ).

tcf(c_99872,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_12,m))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_46106]) ).

tcf(c_99873,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_12,m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99036,c_46104]) ).

tcf(c_99874,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_880]) ).

tcf(c_99875,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_608]) ).

tcf(c_99876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_524]) ).

tcf(c_99877,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_523]) ).

tcf(c_99878,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_347]) ).

tcf(c_99879,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_346]) ).

tcf(c_99880,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_99036,c_254]) ).

tcf(c_99891,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(demodulation,[status(thm)],[c_98872,c_76401]) ).

tcf(c_99892,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_257,c_99891]) ).

tcf(c_99894,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_12,m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_76874,c_99891]) ).

tcf(c_99895,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_256,c_99891]) ).

tcf(c_99897,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_93890,c_99891]) ).

tcf(c_99898,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78930,c_99891]) ).

tcf(c_99899,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,iPr_def_15)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78938,c_99891]) ).

tcf(c_99900,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,iPr_def_14)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79190,c_99891]) ).

tcf(c_99901,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79161,c_99891]) ).

tcf(c_99902,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79901,c_99891]) ).

tcf(c_99903,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_79904,c_99891]) ).

tcf(c_99905,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_85658,c_99891]) ).

tcf(c_99906,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88494,c_99891]) ).

tcf(c_99907,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88513,c_99891]) ).

tcf(c_99908,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_88550,c_99891]) ).

tcf(c_99910,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_92625,c_99891]) ).

tcf(c_99911,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_92936,c_99891]) ).

tcf(c_99924,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_46106]) ).

tcf(c_99925,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_99891,c_46104]) ).

tcf(c_99926,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_880]) ).

tcf(c_99927,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_608]) ).

tcf(c_99928,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_524]) ).

tcf(c_99929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_523]) ).

tcf(c_99930,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_347]) ).

tcf(c_99931,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_346]) ).

tcf(c_99932,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_99891,c_254]) ).

tcf(c_99933,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_99897,c_93903]) ).

tcf(c_99986,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_98014,c_98873]) ).

tcf(c_99987,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),m)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_98873]) ).

tcf(c_99993,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2)))))),
    inference(superposition,[status(thm)],[c_252,c_98873]) ).

tcf(c_100000,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2)))))),
    inference(superposition,[status(thm)],[c_256,c_98873]) ).

tcf(c_100002,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m))))),
    inference(superposition,[status(thm)],[c_93890,c_98873]) ).

tcf(c_100003,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))))))),
    inference(superposition,[status(thm)],[c_78930,c_98873]) ).

tcf(c_100004,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_15))))),
    inference(superposition,[status(thm)],[c_78938,c_98873]) ).

tcf(c_100006,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1))))))),
    inference(superposition,[status(thm)],[c_79161,c_98873]) ).

tcf(c_100007,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14))))))),
    inference(superposition,[status(thm)],[c_79901,c_98873]) ).

tcf(c_100008,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))),
    inference(superposition,[status(thm)],[c_79904,c_98873]) ).

tcf(c_100010,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))),
    inference(superposition,[status(thm)],[c_85658,c_98873]) ).

tcf(c_100011,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88494,c_98873]) ).

tcf(c_100012,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88513,c_98873]) ).

tcf(c_100013,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88550,c_98873]) ).

tcf(c_100015,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_92625,c_98873]) ).

tcf(c_100016,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_92936,c_98873]) ).

tcf(c_100017,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_93551,c_98873]) ).

tcf(c_100029,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2)))),
    inference(superposition,[status(thm)],[c_98873,c_46106]) ).

tcf(c_100030,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98873,c_46104]) ).

tcf(c_100031,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_880]) ).

tcf(c_100032,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_608]) ).

tcf(c_100033,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_524]) ).

tcf(c_100034,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_523]) ).

tcf(c_100035,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_347]) ).

tcf(c_100036,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_346]) ).

tcf(c_100037,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_98873,c_254]) ).

tcf(c_100039,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_99987,c_79190,c_99243]) ).

tcf(c_100040,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_100011,c_88968]) ).

tcf(c_100041,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_100013,c_89827]) ).

tcf(c_100042,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_100012,c_89622]) ).

tcf(c_100121,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),m))))),
    inference(superposition,[status(thm)],[c_98014,c_98879]) ).

tcf(c_100128,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),m)),X2))))),
    inference(superposition,[status(thm)],[c_217,c_98879]) ).

tcf(c_100134,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),X2)))),
    inference(superposition,[status(thm)],[c_255,c_98879]) ).

tcf(c_100135,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0)))),
    inference(superposition,[status(thm)],[c_77148,c_98879]) ).

tcf(c_100138,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),m)),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),m)),X2))),
    inference(superposition,[status(thm)],[c_98879,c_46106]) ).

tcf(c_100139,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),m)),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98879,c_46104]) ).

tcf(c_100140,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_880]) ).

tcf(c_100141,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_608]) ).

tcf(c_100142,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_524]) ).

tcf(c_100143,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_523]) ).

tcf(c_100144,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_347]) ).

tcf(c_100145,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_346]) ).

tcf(c_100146,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_98879,c_254]) ).

tcf(c_100161,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_98014,c_98897]) ).

tcf(c_100162,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))),
    inference(superposition,[status(thm)],[c_79557,c_98897]) ).

tcf(c_100163,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_98897]) ).

tcf(c_100164,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98897]) ).

tcf(c_100167,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X2))))),
    inference(superposition,[status(thm)],[c_217,c_98897]) ).

tcf(c_100170,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))),
    inference(superposition,[status(thm)],[c_76855,c_98897]) ).

tcf(c_100171,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19))),X0)))),
    inference(superposition,[status(thm)],[c_79150,c_98897]) ).

tcf(c_100174,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),X0)))),
    inference(superposition,[status(thm)],[c_76874,c_98897]) ).

tcf(c_100175,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1))),X2)))),
    inference(superposition,[status(thm)],[c_256,c_98897]) ).

tcf(c_100177,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_93890,c_98897]) ).

tcf(c_100187,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X2))),
    inference(superposition,[status(thm)],[c_98897,c_46106]) ).

tcf(c_100188,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1)),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98897,c_46104]) ).

tcf(c_100189,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_880]) ).

tcf(c_100190,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_608]) ).

tcf(c_100191,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_524]) ).

tcf(c_100192,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_523]) ).

tcf(c_100193,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_347]) ).

tcf(c_100194,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_346]) ).

tcf(c_100195,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_98897,c_254]) ).

tcf(c_100196,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_100163,c_94398]) ).

tcf(c_100197,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))),
    inference(light_normalisation,[status(thm)],[c_100162,c_94398]) ).

tcf(c_100234,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m))))),
    inference(superposition,[status(thm)],[c_98014,c_98898]) ).

tcf(c_100235,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_98014,c_98898]) ).

tcf(c_100236,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79557,c_98898]) ).

tcf(c_100237,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_98898]) ).

tcf(c_100238,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98898]) ).

tcf(c_100241,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X2))))),
    inference(superposition,[status(thm)],[c_217,c_98898]) ).

tcf(c_100244,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_76855,c_98898]) ).

tcf(c_100248,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19)))),X2)))),
    inference(superposition,[status(thm)],[c_255,c_98898]) ).

tcf(c_100251,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X2))),
    inference(superposition,[status(thm)],[c_98898,c_46106]) ).

tcf(c_100252,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),sK30(iPr_def_19))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98898,c_46104]) ).

tcf(c_100253,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_880]) ).

tcf(c_100254,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_608]) ).

tcf(c_100255,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_524]) ).

tcf(c_100256,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_523]) ).

tcf(c_100257,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_347]) ).

tcf(c_100258,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_346]) ).

tcf(c_100259,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_98898,c_254]) ).

tcf(c_100260,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_100237,c_94485]) ).

tcf(c_100261,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_100236,c_94485]) ).

tcf(c_100298,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))))),
    inference(superposition,[status(thm)],[c_79557,c_99237]) ).

tcf(c_100300,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))))),
    inference(superposition,[status(thm)],[c_82861,c_99237]) ).

tcf(c_100301,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))),
    inference(superposition,[status(thm)],[c_253,c_99237]) ).

tcf(c_100303,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))),
    inference(superposition,[status(thm)],[c_217,c_99237]) ).

tcf(c_100305,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(pls)))),
    inference(superposition,[status(thm)],[c_1001,c_99237]) ).

tcf(c_100306,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))))),
    inference(superposition,[status(thm)],[c_76855,c_99237]) ).

tcf(c_100307,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))),
    inference(superposition,[status(thm)],[c_83532,c_99237]) ).

tcf(c_100308,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))))),
    inference(superposition,[status(thm)],[c_257,c_99237]) ).

tcf(c_100310,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))))),
    inference(superposition,[status(thm)],[c_76874,c_99237]) ).

tcf(c_100311,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))))),
    inference(superposition,[status(thm)],[c_256,c_99237]) ).

tcf(c_100313,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1))))),
    inference(superposition,[status(thm)],[c_93890,c_99237]) ).

tcf(c_100314,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1))))),
    inference(superposition,[status(thm)],[c_78930,c_99237]) ).

tcf(c_100315,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))))),
    inference(superposition,[status(thm)],[c_78938,c_99237]) ).

tcf(c_100316,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))))),
    inference(superposition,[status(thm)],[c_79190,c_99237]) ).

tcf(c_100317,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1))))),
    inference(superposition,[status(thm)],[c_79161,c_99237]) ).

tcf(c_100318,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1))))),
    inference(superposition,[status(thm)],[c_79901,c_99237]) ).

tcf(c_100319,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))))),
    inference(superposition,[status(thm)],[c_79904,c_99237]) ).

tcf(c_100321,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))))),
    inference(superposition,[status(thm)],[c_85658,c_99237]) ).

tcf(c_100322,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))))),
    inference(superposition,[status(thm)],[c_88494,c_99237]) ).

tcf(c_100323,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_88513,c_99237]) ).

tcf(c_100324,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_88550,c_99237]) ).

tcf(c_100326,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))))),
    inference(superposition,[status(thm)],[c_92625,c_99237]) ).

tcf(c_100327,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_92936,c_99237]) ).

tcf(c_100328,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))))),
    inference(superposition,[status(thm)],[c_93551,c_99237]) ).

tcf(c_100340,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_99237,c_46106]) ).

tcf(c_100341,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99237,c_46104]) ).

tcf(c_100342,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_880]) ).

tcf(c_100343,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_608]) ).

tcf(c_100344,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_524]) ).

tcf(c_100345,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_523]) ).

tcf(c_100346,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_347]) ).

tcf(c_100347,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_346]) ).

tcf(c_100348,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_99237,c_254]) ).

tcf(c_100350,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_100328,c_79573]) ).

tcf(c_100351,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0))))),
    inference(light_normalisation,[status(thm)],[c_100316,c_99243]) ).

tcf(c_100352,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),
    inference(light_normalisation,[status(thm)],[c_100298,c_79918]) ).

tcf(c_100353,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1))))),
    inference(light_normalisation,[status(thm)],[c_100313,c_93903,c_99172]) ).

tcf(c_100354,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))))),
    inference(light_normalisation,[status(thm)],[c_100322,c_88957]) ).

tcf(c_100355,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))))),
    inference(light_normalisation,[status(thm)],[c_100324,c_89816]) ).

tcf(c_100356,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))))),
    inference(light_normalisation,[status(thm)],[c_100323,c_89611]) ).

tcf(c_100432,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(pls),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_574,c_83534]) ).

tcf(c_100433,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76397,c_83534]) ).

tcf(c_100434,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(one_one_int),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76393,c_83534]) ).

tcf(c_100435,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(undefined_int(int)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(undefined_int(int)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76395,c_83534]) ).

tcf(c_100436,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_76399,c_83534]) ).

tcf(c_100437,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(X0,X1)),hAPP_int_int(plus_plus_int(m),X2))),
    inference(superposition,[status(thm)],[c_76401,c_83534]) ).

tcf(c_100438,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76402,c_83534]) ).

tcf(c_100439,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(s1),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(s1),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76403,c_83534]) ).

tcf(c_100440,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(s),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(s),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76404,c_83534]) ).

tcf(c_100441,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(t),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(t),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76405,c_83534]) ).

tcf(c_100442,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK9),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK9),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76406,c_83534]) ).

tcf(c_100443,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK10),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK10),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76407,c_83534]) ).

tcf(c_100444,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK11),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK11),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76408,c_83534]) ).

tcf(c_100445,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK13),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK13),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76409,c_83534]) ).

tcf(c_100446,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76410,c_83534]) ).

tcf(c_100447,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_15),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_15),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76411,c_83534]) ).

tcf(c_100448,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_16),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_16),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76412,c_83534]) ).

tcf(c_100449,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_17),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_17),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76413,c_83534]) ).

tcf(c_100450,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(iPr_def_18),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(iPr_def_18),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76414,c_83534]) ).

tcf(c_100451,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76415,c_83534]) ).

tcf(c_100452,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_77366,c_83534]) ).

tcf(c_100453,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK26(iPr_def_14)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_78203,c_83534]) ).

tcf(c_100454,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79573,c_83534]) ).

tcf(c_100455,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79414,c_83534]) ).

tcf(c_100456,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79557,c_83534]) ).

tcf(c_100457,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79437,c_83534]) ).

tcf(c_100459,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_83504,c_83534]) ).

tcf(c_100460,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_83534]) ).

tcf(c_100461,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80677,c_83534]) ).

tcf(c_100462,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80692,c_83534]) ).

tcf(c_100463,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80705,c_83534]) ).

tcf(c_100464,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_88502,c_83534]) ).

tcf(c_100465,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_88521,c_83534]) ).

tcf(c_100466,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_88558,c_83534]) ).

tcf(c_100467,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_83534]) ).

tcf(c_100468,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93822,c_83534]) ).

tcf(c_100469,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94573,c_83534]) ).

tcf(c_100470,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94594,c_83534]) ).

tcf(c_100471,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94672,c_83534]) ).

tcf(c_100472,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94695,c_83534]) ).

tcf(c_100473,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95015,c_83534]) ).

tcf(c_100474,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95041,c_83534]) ).

tcf(c_100475,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95257,c_83534]) ).

tcf(c_100476,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95286,c_83534]) ).

tcf(c_100477,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95382,c_83534]) ).

tcf(c_100478,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95414,c_83534]) ).

tcf(c_100479,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),pls)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),pls))),
    inference(superposition,[status(thm)],[c_574,c_83534]) ).

tcf(c_100480,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),min)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),min))),
    inference(superposition,[status(thm)],[c_76397,c_83534]) ).

tcf(c_100481,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),one_one_int)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_83534]) ).

tcf(c_100482,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),undefined_int(int))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_83534]) ).

tcf(c_100483,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1)))),
    inference(superposition,[status(thm)],[c_76399,c_83534]) ).

tcf(c_100484,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2)))),
    inference(superposition,[status(thm)],[c_76401,c_83534]) ).

tcf(c_100485,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),m)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),m))),
    inference(superposition,[status(thm)],[c_76402,c_83534]) ).

tcf(c_100486,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),s1)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),s1))),
    inference(superposition,[status(thm)],[c_76403,c_83534]) ).

tcf(c_100487,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),s)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),s))),
    inference(superposition,[status(thm)],[c_76404,c_83534]) ).

tcf(c_100488,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),t)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),t))),
    inference(superposition,[status(thm)],[c_76405,c_83534]) ).

tcf(c_100489,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK9)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_83534]) ).

tcf(c_100490,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK10)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_83534]) ).

tcf(c_100491,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK11)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_83534]) ).

tcf(c_100492,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK13)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_83534]) ).

tcf(c_100493,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_14)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_83534]) ).

tcf(c_100494,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_15)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_83534]) ).

tcf(c_100495,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_16)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_83534]) ).

tcf(c_100496,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_17)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_83534]) ).

tcf(c_100497,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_18)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_83534]) ).

tcf(c_100498,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76415,c_83534]) ).

tcf(c_100499,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1)))),
    inference(superposition,[status(thm)],[c_77366,c_83534]) ).

tcf(c_100500,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_83534]) ).

tcf(c_100501,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79573,c_83534]) ).

tcf(c_100502,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79414,c_83534]) ).

tcf(c_100503,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79557,c_83534]) ).

tcf(c_100504,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_83534]) ).

tcf(c_100505,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79918,c_83534]) ).

tcf(c_100506,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_83504,c_83534]) ).

tcf(c_100507,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80664,c_83534]) ).

tcf(c_100508,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_80677,c_83534]) ).

tcf(c_100509,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_80692,c_83534]) ).

tcf(c_100510,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_83534]) ).

tcf(c_100511,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_83534]) ).

tcf(c_100512,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_83534]) ).

tcf(c_100513,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_83534]) ).

tcf(c_100514,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),X0))))
      | ~ is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_83534,c_65]) ).

tcf(c_100515,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))
      | ~ hBOOL(hAPP_int_bool(zcong(number_number_of_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),X2)) ),
    inference(superposition,[status(thm)],[c_83534,c_897]) ).

tcf(c_100516,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(number_number_of_int(X1),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2))),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),X2))))) ),
    inference(superposition,[status(thm)],[c_83534,c_896]) ).

tcf(c_100519,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_100485,c_79190]) ).

tcf(c_100766,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X1),X2)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_801,c_1025]) ).

tcf(c_100769,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(X0),X1)),X2))),
    inference(superposition,[status(thm)],[c_1043,c_1025]) ).

tcf(c_100773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_975,c_1025]) ).

tcf(c_100774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),X3))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(times_times_real(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_219,c_1025]) ).

tcf(c_100779,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X1),one_one_real)),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X0),hAPP_real_real(times_times_real(X1),X0))),X2)) ),
    inference(superposition,[status(thm)],[c_370,c_1025]) ).

tcf(c_100781,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(X0)),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(hAPP_int_int(times_times_int(X0),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_383,c_1025]) ).

tcf(c_100782,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,number267125858f_real(hAPP_int_int(plus_plus_int(X0),X0))),X1)) ),
    inference(superposition,[status(thm)],[c_408,c_1025]) ).

tcf(c_100795,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(plus_plus_real(X1),one_one_real)),X2))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),hAPP_real_real(plus_plus_real(X1),one_one_real))),X2)) ),
    inference(light_normalisation,[status(thm)],[c_100779,c_94193]) ).

tcf(c_100806,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_803,c_1026]) ).

tcf(c_100809,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2))),
    inference(superposition,[status(thm)],[c_1044,c_1026]) ).

tcf(c_100811,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),sK35(X2,hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1577,c_1026]) ).

tcf(c_100812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(div_mod_nat(X0),X3)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X1),X2)),X3) ),
    inference(superposition,[status(thm)],[c_1711,c_1026]) ).

tcf(c_100815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_218,c_1026]) ).

tcf(c_100822,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))),
    inference(light_normalisation,[status(thm)],[c_100809,c_91270]) ).

tcf(c_100833,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X2))
      | is_int(sK30(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)))) ),
    inference(superposition,[status(thm)],[c_1563,c_1027]) ).

tcf(c_100834,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X1),X2)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_805,c_1027]) ).

tcf(c_100835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(minus_minus_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(zcong(X0,X1),hAPP_int_int(times_times_int(X2),X3))) ),
    inference(superposition,[status(thm)],[c_897,c_1027]) ).

tcf(c_100838,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2))),
    inference(superposition,[status(thm)],[c_1045,c_1027]) ).

tcf(c_100840,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),X1)))),
    inference(superposition,[status(thm)],[c_76497,c_1027]) ).

tcf(c_100841,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1720,c_1027]) ).

tcf(c_100845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_252,c_1027]) ).

tcf(c_100846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_217,c_1027]) ).

tcf(c_100849,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_382,c_1027]) ).

tcf(c_100859,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,twoSqu1241645765sum2sq(X0)),X1)) ),
    inference(superposition,[status(thm)],[c_77069,c_1027]) ).

tcf(c_100860,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,iPr_def_14),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(X0),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79150,c_1027]) ).

tcf(c_100861,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)) ),
    inference(superposition,[status(thm)],[c_83532,c_1027]) ).

tcf(c_100863,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_88519,c_1027]) ).

tcf(c_100864,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)) ),
    inference(superposition,[status(thm)],[c_88556,c_1027]) ).

tcf(c_100865,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)) ),
    inference(superposition,[status(thm)],[c_96186,c_1027]) ).

tcf(c_100866,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) ),
    inference(superposition,[status(thm)],[c_98014,c_1027]) ).

tcf(c_100867,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(iPr_def_19)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) ),
    inference(superposition,[status(thm)],[c_98014,c_1027]) ).

tcf(c_100933,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_nat_real(power_power_real(X1),iPr_def_11)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_82839,c_1034]) ).

tcf(c_100935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X3),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_975,c_1034]) ).

tcf(c_100936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X3),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X2))) ),
    inference(superposition,[status(thm)],[c_219,c_1034]) ).

tcf(c_100939,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),one_one_real)) ),
    inference(superposition,[status(thm)],[c_325,c_1034]) ).

tcf(c_100941,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X1),hAPP_real_real(times_times_real(X2),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_370,c_1034]) ).

tcf(c_100942,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X1),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_373,c_1034]) ).

tcf(c_100943,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(X1))) ),
    inference(superposition,[status(thm)],[c_383,c_1034]) ).

tcf(c_100944,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(X1))) ),
    inference(superposition,[status(thm)],[c_408,c_1034]) ).

tcf(c_100947,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X1),X1)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))) ),
    inference(superposition,[status(thm)],[c_14792,c_1034]) ).

tcf(c_100948,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(X1),X0) = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_1034,c_1017]) ).

tcf(c_100949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X3),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1034,c_1025]) ).

tcf(c_100950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X3),X2)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1034,c_1022]) ).

tcf(c_101004,plain,
    ~ hBOOL(member_int(iPr_def_14,d22set(one_one_int))),
    inference(superposition,[status(thm)],[c_59638,c_94943]) ).

tcf(c_101008,plain,
    ~ hBOOL(member_int(min,d22set(hAPP_int_int(plus_plus_int(min),min)))),
    inference(superposition,[status(thm)],[c_76610,c_94943]) ).

tcf(c_101010,plain,
    ~ hBOOL(member_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),d22set(hAPP_int_int(times_times_int(s),s)))),
    inference(superposition,[status(thm)],[c_82935,c_94943]) ).

tcf(c_101011,plain,
    ~ hBOOL(member_int(sK30(iPr_def_19),d22set(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)))),
    inference(superposition,[status(thm)],[c_83830,c_94943]) ).

tcf(c_101012,plain,
    is_int(sK30(d22set(one_one_int))),
    inference(superposition,[status(thm)],[c_76445,c_101004]) ).

tcf(c_101015,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_79414,c_98875]) ).

tcf(c_101016,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98875]) ).

tcf(c_101017,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),X2)))),
    inference(superposition,[status(thm)],[c_253,c_98875]) ).

tcf(c_101020,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),X2))))),
    inference(superposition,[status(thm)],[c_217,c_98875]) ).

tcf(c_101023,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_59637,c_98875]) ).

tcf(c_101024,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11))))),
    inference(superposition,[status(thm)],[c_82861,c_98875]) ).

tcf(c_101027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))))),
    inference(superposition,[status(thm)],[c_217,c_98875]) ).

tcf(c_101029,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),pls)))),
    inference(superposition,[status(thm)],[c_1001,c_98875]) ).

tcf(c_101030,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X1)))))),
    inference(superposition,[status(thm)],[c_76855,c_98875]) ).

tcf(c_101031,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))),
    inference(superposition,[status(thm)],[c_83532,c_98875]) ).

tcf(c_101035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2))),X3))))),
    inference(superposition,[status(thm)],[c_256,c_98875]) ).

tcf(c_101037,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m)),X2))))),
    inference(superposition,[status(thm)],[c_93890,c_98875]) ).

tcf(c_101038,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X2))))),
    inference(superposition,[status(thm)],[c_78930,c_98875]) ).

tcf(c_101039,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X1))))),
    inference(superposition,[status(thm)],[c_78938,c_98875]) ).

tcf(c_101040,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X1))))),
    inference(superposition,[status(thm)],[c_79190,c_98875]) ).

tcf(c_101041,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),X2))))),
    inference(superposition,[status(thm)],[c_79161,c_98875]) ).

tcf(c_101042,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),X2))))),
    inference(superposition,[status(thm)],[c_79901,c_98875]) ).

tcf(c_101043,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X1))))),
    inference(superposition,[status(thm)],[c_79904,c_98875]) ).

tcf(c_101045,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))))),
    inference(superposition,[status(thm)],[c_85658,c_98875]) ).

tcf(c_101046,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_88494,c_98875]) ).

tcf(c_101047,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X2))))),
    inference(superposition,[status(thm)],[c_88513,c_98875]) ).

tcf(c_101048,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X2))))),
    inference(superposition,[status(thm)],[c_88550,c_98875]) ).

tcf(c_101052,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_93551,c_98875]) ).

tcf(c_101064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))),
    inference(superposition,[status(thm)],[c_98875,c_46106]) ).

tcf(c_101065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98875,c_46104]) ).

tcf(c_101066,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_880]) ).

tcf(c_101067,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_608]) ).

tcf(c_101068,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_524]) ).

tcf(c_101069,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_523]) ).

tcf(c_101070,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_347]) ).

tcf(c_101071,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_346]) ).

tcf(c_101072,plain,
    ! [X0: $i,X1: $i,X2: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98875,c_254]) ).

tcf(c_101074,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_101052,c_90934]) ).

tcf(c_101131,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),X1)),m))))),
    inference(superposition,[status(thm)],[c_98014,c_98882]) ).

tcf(c_101132,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2)))))),
    inference(superposition,[status(thm)],[c_98014,c_98882]) ).

tcf(c_101133,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))),
    inference(superposition,[status(thm)],[c_79557,c_98882]) ).

tcf(c_101134,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_98882]) ).

tcf(c_101135,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_98882]) ).

tcf(c_101141,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))),
    inference(superposition,[status(thm)],[c_76855,c_98882]) ).

tcf(c_101142,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),X0))),X1)))),
    inference(superposition,[status(thm)],[c_79150,c_98882]) ).

tcf(c_101143,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),X0)),X1)),X2)))),
    inference(superposition,[status(thm)],[c_257,c_98882]) ).

tcf(c_101146,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))),X2)))),
    inference(superposition,[status(thm)],[c_256,c_98882]) ).

tcf(c_101149,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))),
    inference(superposition,[status(thm)],[c_92925,c_98882]) ).

tcf(c_101151,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(m),X0))),X1)))),
    inference(superposition,[status(thm)],[c_59636,c_98882]) ).

tcf(c_101154,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,m))),X1)))),
    inference(superposition,[status(thm)],[c_76874,c_98882]) ).

tcf(c_101155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2)))),X3)))),
    inference(superposition,[status(thm)],[c_256,c_98882]) ).

tcf(c_101157,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m))),X2)))),
    inference(superposition,[status(thm)],[c_93890,c_98882]) ).

tcf(c_101158,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1))))),X2)))),
    inference(superposition,[status(thm)],[c_78930,c_98882]) ).

tcf(c_101159,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_15))),X1)))),
    inference(superposition,[status(thm)],[c_78938,c_98882]) ).

tcf(c_101160,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),X1)))),
    inference(superposition,[status(thm)],[c_79190,c_98882]) ).

tcf(c_101161,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1))))),X2)))),
    inference(superposition,[status(thm)],[c_79161,c_98882]) ).

tcf(c_101162,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14))))),X2)))),
    inference(superposition,[status(thm)],[c_79901,c_98882]) ).

tcf(c_101163,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))),X1)))),
    inference(superposition,[status(thm)],[c_79904,c_98882]) ).

tcf(c_101165,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X1)))),
    inference(superposition,[status(thm)],[c_85658,c_98882]) ).

tcf(c_101166,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X1)))),
    inference(superposition,[status(thm)],[c_88494,c_98882]) ).

tcf(c_101167,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),X2)))),
    inference(superposition,[status(thm)],[c_88513,c_98882]) ).

tcf(c_101168,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),X2)))),
    inference(superposition,[status(thm)],[c_88550,c_98882]) ).

tcf(c_101184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2))),X3)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2))),X3))),
    inference(superposition,[status(thm)],[c_98882,c_46106]) ).

tcf(c_101185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(m),X2))),X3))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98882,c_46104]) ).

tcf(c_101186,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_880]) ).

tcf(c_101187,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_608]) ).

tcf(c_101188,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_524]) ).

tcf(c_101189,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_523]) ).

tcf(c_101190,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_347]) ).

tcf(c_101191,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_346]) ).

tcf(c_101192,plain,
    ! [X0: $i,X1: $i,X2: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_98882,c_254]) ).

tcf(c_101193,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_101149,c_99171]) ).

tcf(c_101194,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)))),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_101134,c_92987]) ).

tcf(c_101195,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)))))),
    inference(light_normalisation,[status(thm)],[c_101133,c_92987]) ).

tcf(c_101354,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))),number_number_of_int(X0))))),
    inference(demodulation,[status(thm)],[c_98890,c_79415,c_90827,c_91959]) ).

tcf(c_101356,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79573,c_99028]) ).

tcf(c_101357,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_79414,c_99028]) ).

tcf(c_101358,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_99028]) ).

tcf(c_101359,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))),X2)))),
    inference(superposition,[status(thm)],[c_253,c_99028]) ).

tcf(c_101366,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),m)),iPr_def_11))))),
    inference(superposition,[status(thm)],[c_82861,c_99028]) ).

tcf(c_101369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),
    inference(superposition,[status(thm)],[c_252,c_99028]) ).

tcf(c_101371,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_59637,c_99028]) ).

tcf(c_101374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),
    inference(superposition,[status(thm)],[c_255,c_99028]) ).

tcf(c_101375,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),m))))),
    inference(superposition,[status(thm)],[c_77148,c_99028]) ).

tcf(c_101376,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_13,iPr_def_14)))))),
    inference(superposition,[status(thm)],[c_79190,c_99028]) ).

tcf(c_101378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m)))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))),
    inference(superposition,[status(thm)],[c_99028,c_46106]) ).

tcf(c_101379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99028,c_46104]) ).

tcf(c_101380,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_880]) ).

tcf(c_101381,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_608]) ).

tcf(c_101382,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_524]) ).

tcf(c_101383,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_523]) ).

tcf(c_101384,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_347]) ).

tcf(c_101385,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_346]) ).

tcf(c_101386,plain,
    ! [X0: $i,X1: $i,X2: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99028,c_254]) ).

tcf(c_101387,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),X1))))),
    inference(light_normalisation,[status(thm)],[c_101375,c_91991]) ).

tcf(c_101466,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_98014,c_99033]) ).

tcf(c_101467,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79573,c_99033]) ).

tcf(c_101468,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_79414,c_99033]) ).

tcf(c_101469,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m))),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_99033]) ).

tcf(c_101474,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_59637,c_99033]) ).

tcf(c_101475,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_79150,c_99033]) ).

tcf(c_101476,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),m)),X2))))),
    inference(superposition,[status(thm)],[c_257,c_99033]) ).

tcf(c_101483,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_59636,c_99033]) ).

tcf(c_101486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),
    inference(superposition,[status(thm)],[c_255,c_99033]) ).

tcf(c_101488,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_13,iPr_def_14)))))),
    inference(superposition,[status(thm)],[c_79190,c_99033]) ).

tcf(c_101489,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(iPr_def_12,m)))))),
    inference(superposition,[status(thm)],[c_59636,c_99033]) ).

tcf(c_101490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X3),m)))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X3),m))))),
    inference(superposition,[status(thm)],[c_99033,c_46106]) ).

tcf(c_101491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99033,c_46104]) ).

tcf(c_101492,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_880]) ).

tcf(c_101493,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_608]) ).

tcf(c_101494,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_524]) ).

tcf(c_101495,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_523]) ).

tcf(c_101496,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_347]) ).

tcf(c_101497,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_346]) ).

tcf(c_101498,plain,
    ! [X0: $i,X1: $i,X2: $i] : number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99033,c_254]) ).

tcf(c_101517,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))),number_number_of_int(X1))))),
    inference(demodulation,[status(thm)],[c_98885,c_79415,c_90827,c_91959]) ).

tcf(c_101518,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))),number_number_of_int(X1))))),
    inference(demodulation,[status(thm)],[c_98888,c_79415,c_90827,c_91959]) ).

tcf(c_101519,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))),number_number_of_int(X1))))),
    inference(demodulation,[status(thm)],[c_98889,c_79415,c_90827,c_91959]) ).

tcf(c_101520,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1))),
    inference(light_normalisation,[status(thm)],[c_83535,c_86126,c_92987]) ).

tcf(c_101525,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(power_power_nat(X1),iPr_def_11)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_82316,c_1035]) ).

tcf(c_101527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X3),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_218,c_1035]) ).

tcf(c_101530,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_1413,c_1035]) ).

tcf(c_101534,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1035,c_1590]) ).

tcf(c_101535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X3),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1035,c_1026]) ).

tcf(c_101536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X3),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1035,c_1023]) ).

tcf(c_101557,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X2),X1)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_1036]) ).

tcf(c_101558,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(X1),iPr_def_11)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_82861,c_1036]) ).

tcf(c_101561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X3),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_252,c_1036]) ).

tcf(c_101562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X3),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(superposition,[status(thm)],[c_217,c_1036]) ).

tcf(c_101565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_382,c_1036]) ).

tcf(c_101567,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_79464,c_1036]) ).

tcf(c_101568,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(iPr_def_13,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),m)) ),
    inference(superposition,[status(thm)],[c_76855,c_1036]) ).

tcf(c_101569,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_15))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76925,c_1036]) ).

tcf(c_101570,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_16))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76926,c_1036]) ).

tcf(c_101571,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_17))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76927,c_1036]) ).

tcf(c_101572,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_18))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76928,c_1036]) ).

tcf(c_101576,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_79150,c_1036]) ).

tcf(c_101577,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_83532,c_1036]) ).

tcf(c_101581,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X1))))) ),
    inference(superposition,[status(thm)],[c_96186,c_1036]) ).

tcf(c_101582,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))) ),
    inference(superposition,[status(thm)],[c_98014,c_1036]) ).

tcf(c_101583,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))) ),
    inference(superposition,[status(thm)],[c_98014,c_1036]) ).

tcf(c_101584,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(iPr_def_13,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_59637,c_1036]) ).

tcf(c_101585,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(hAPP_int_int(times_times_int(X2),X1),hAPP_i1948725293t_bool(dvd_dvd_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1036,c_226]) ).

tcf(c_101586,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X2),X1),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1036,c_929]) ).

tcf(c_101587,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X1),X0) = pls )
      | ~ is_int(hAPP_int_int(times_times_int(X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1036,c_1019]) ).

tcf(c_101588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X3),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1036,c_1027]) ).

tcf(c_101589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X3),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1036,c_1024]) ).

tcf(c_101698,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),hAPP_real_real(times_times_real(X2),X3))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X1),X2))) ),
    inference(superposition,[status(thm)],[c_975,c_1037]) ).

tcf(c_101699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X2),hAPP_real_real(times_times_real(X1),X3))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_219,c_1037]) ).

tcf(c_101704,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X2),hAPP_real_real(times_times_real(X1),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(X1),one_one_real))) ),
    inference(superposition,[status(thm)],[c_370,c_1037]) ).

tcf(c_101706,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(hAPP_int_int(times_times_int(X1),X2))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(X1))) ),
    inference(superposition,[status(thm)],[c_383,c_1037]) ).

tcf(c_101707,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),number267125858f_real(hAPP_int_int(plus_plus_int(X1),X1))))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))) ),
    inference(superposition,[status(thm)],[c_408,c_1037]) ).

tcf(c_101711,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_real_real(times_times_real(X0),X1) = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_1037,c_1017]) ).

tcf(c_101712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X0),hAPP_real_real(times_times_real(X2),X3)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1037,c_1025]) ).

tcf(c_101713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X1),hAPP_real_real(times_times_real(X2),X3)))
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1037,c_1022]) ).

tcf(c_101737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X1),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_218,c_1038]) ).

tcf(c_101744,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1038,c_1590]) ).

tcf(c_101745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X2),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1038,c_1026]) ).

tcf(c_101746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(times_times_nat(X2),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1038,c_1023]) ).

tcf(c_101758,plain,
    hBOOL(member_int(iPr_def_14,hAPP_i1948725293t_bool(ord_less_int,one_one_int))),
    inference(superposition,[status(thm)],[c_59638,c_94944]) ).

tcf(c_101762,plain,
    hBOOL(member_int(min,hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(min),min)))),
    inference(superposition,[status(thm)],[c_76610,c_94944]) ).

tcf(c_101764,plain,
    hBOOL(member_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)))),
    inference(superposition,[status(thm)],[c_82935,c_94944]) ).

tcf(c_101765,plain,
    hBOOL(member_int(sK30(iPr_def_19),hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),one_one_int)))),
    inference(superposition,[status(thm)],[c_83830,c_94944]) ).

tcf(c_101766,plain,
    hBOOL(member_int(hAPP_int_int(iPr_def_12,one_one_int),iPr_def_19)),
    inference(superposition,[status(thm)],[c_59643,c_94944]) ).

tcf(c_101771,plain,
    ! [X0: $i] : is_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),X0)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_94966]) ).

tcf(c_101772,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),X0)),X1)),
    inference(superposition,[status(thm)],[c_253,c_94966]) ).

tcf(c_101774,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),X2)))),
    inference(superposition,[status(thm)],[c_252,c_94966]) ).

tcf(c_101776,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),
    inference(superposition,[status(thm)],[c_59637,c_94966]) ).

tcf(c_101779,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X2))))),
    inference(superposition,[status(thm)],[c_255,c_94966]) ).

tcf(c_101780,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X2)))),
    inference(superposition,[status(thm)],[c_256,c_94966]) ).

tcf(c_101783,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_388,c_94966]) ).

tcf(c_101785,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,one_one_int))),
    inference(superposition,[status(thm)],[c_59636,c_94966]) ).

tcf(c_101786,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),X2))),X0)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),X2)),
    inference(superposition,[status(thm)],[c_94966,c_46106]) ).

tcf(c_101787,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),X2)))),X0) = pls,
    inference(superposition,[status(thm)],[c_94966,c_46104]) ).

tcf(c_101788,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_880]) ).

tcf(c_101789,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),one_one_nat) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_608]) ).

tcf(c_101790,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),pls) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_524]) ).

tcf(c_101791,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_523]) ).

tcf(c_101792,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_347]) ).

tcf(c_101793,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))),one_one_int) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_346]) ).

tcf(c_101794,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),X1)),
    inference(superposition,[status(thm)],[c_94966,c_254]) ).

tcf(c_101835,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK14(X2,X0,min)),X1)) = sK14(X2,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_46106]) ).

tcf(c_101836,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X1),sK14(X2,X0,min))),X1) = pls )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_46104]) ).

tcf(c_101837,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK14(X1,X0,min)),pls) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_880]) ).

tcf(c_101838,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(sK14(X1,X0,min)),one_one_nat) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_608]) ).

tcf(c_101839,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(X1,X0,min)),pls) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_524]) ).

tcf(c_101840,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(pls),sK14(X1,X0,min)) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_523]) ).

tcf(c_101841,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(one_one_int),sK14(X1,X0,min)) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_347]) ).

tcf(c_101842,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(X1,X0,min)),one_one_int) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_346]) ).

tcf(c_101843,plain,
    ! [X0: $i,X1: $i] :
      ( ( number_number_of_int(sK14(X1,X0,min)) = sK14(X1,X0,min) )
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_97803,c_254]) ).

tcf(c_101891,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(demodulation,[status(thm)],[c_98892,c_676,c_253,c_79573,c_82864,c_90800,c_90801,c_91937,c_91938]) ).

tcf(c_101892,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_253,c_101891]) ).

tcf(c_101894,plain,
    is_int(hAPP_int_int(times_times_int(pls),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_574,c_101891]) ).

tcf(c_101895,plain,
    is_int(hAPP_int_int(times_times_int(min),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76397,c_101891]) ).

tcf(c_101896,plain,
    is_int(hAPP_int_int(times_times_int(one_one_int),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76393,c_101891]) ).

tcf(c_101897,plain,
    is_int(hAPP_int_int(times_times_int(undefined_int(int)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76395,c_101891]) ).

tcf(c_101898,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76399,c_101891]) ).

tcf(c_101899,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76401,c_101891]) ).

tcf(c_101900,plain,
    is_int(hAPP_int_int(times_times_int(m),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76402,c_101891]) ).

tcf(c_101901,plain,
    is_int(hAPP_int_int(times_times_int(s1),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76403,c_101891]) ).

tcf(c_101902,plain,
    is_int(hAPP_int_int(times_times_int(s),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76404,c_101891]) ).

tcf(c_101903,plain,
    is_int(hAPP_int_int(times_times_int(t),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76405,c_101891]) ).

tcf(c_101904,plain,
    is_int(hAPP_int_int(times_times_int(sK9),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76406,c_101891]) ).

tcf(c_101905,plain,
    is_int(hAPP_int_int(times_times_int(sK10),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76407,c_101891]) ).

tcf(c_101906,plain,
    is_int(hAPP_int_int(times_times_int(sK11),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76408,c_101891]) ).

tcf(c_101907,plain,
    is_int(hAPP_int_int(times_times_int(sK13),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76409,c_101891]) ).

tcf(c_101908,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76410,c_101891]) ).

tcf(c_101909,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76411,c_101891]) ).

tcf(c_101910,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76412,c_101891]) ).

tcf(c_101911,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76413,c_101891]) ).

tcf(c_101912,plain,
    is_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76414,c_101891]) ).

tcf(c_101913,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_76415,c_101891]) ).

tcf(c_101914,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_77366,c_101891]) ).

tcf(c_101915,plain,
    is_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_78203,c_101891]) ).

tcf(c_101917,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_79414,c_101891]) ).

tcf(c_101919,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_79437,c_101891]) ).

tcf(c_101920,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_79918,c_101891]) ).

tcf(c_101922,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_80664,c_101891]) ).

tcf(c_101923,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_80677,c_101891]) ).

tcf(c_101924,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_80692,c_101891]) ).

tcf(c_101925,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_80705,c_101891]) ).

tcf(c_101926,plain,
    is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_88502,c_101891]) ).

tcf(c_101927,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_88521,c_101891]) ).

tcf(c_101928,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_88558,c_101891]) ).

tcf(c_101929,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),X0)) = hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_46106]) ).

tcf(c_101930,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))))),X0) = pls,
    inference(superposition,[status(thm)],[c_101891,c_46104]) ).

tcf(c_101931,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_880]) ).

tcf(c_101932,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),one_one_nat) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_608]) ).

tcf(c_101933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_524]) ).

tcf(c_101934,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_523]) ).

tcf(c_101935,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_347]) ).

tcf(c_101936,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),one_one_int) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_346]) ).

tcf(c_101937,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101891,c_254]) ).

tcf(c_101938,plain,
    is_int(hAPP_int_int(iPr_def_13,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(light_normalisation,[status(thm)],[c_101900,c_59637]) ).

tcf(c_102046,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_46106]) ).

tcf(c_102047,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))))),X0) = pls,
    inference(superposition,[status(thm)],[c_101913,c_46104]) ).

tcf(c_102048,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_880]) ).

tcf(c_102049,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_608]) ).

tcf(c_102050,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_524]) ).

tcf(c_102051,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_523]) ).

tcf(c_102052,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_347]) ).

tcf(c_102053,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),one_one_int) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_346]) ).

tcf(c_102054,plain,
    number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11))),
    inference(superposition,[status(thm)],[c_101913,c_254]) ).

tcf(c_102072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),hAPP_nat_nat(times_times_nat(iPr_def_11),X4))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96465]) ).

tcf(c_102079,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),zero_zero_nat)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96465]) ).

tcf(c_102081,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(iPr_def_11),X2) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96465]) ).

tcf(c_102085,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(iPr_def_11),X4)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96465]) ).

tcf(c_102109,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96474]) ).

tcf(c_102110,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96474]) ).

tcf(c_102113,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96474]) ).

tcf(c_102116,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X2)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_82316,c_96474]) ).

tcf(c_102118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(times_times_nat(X2),X3)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96474]) ).

tcf(c_102120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X2)),X3))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96474]) ).

tcf(c_102124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(iPr_def_11),X4))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_218,c_96474]) ).

tcf(c_102129,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_102110,c_59636]) ).

tcf(c_102132,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_102109,c_78498]) ).

tcf(c_102215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96510]) ).

tcf(c_102216,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96510]) ).

tcf(c_102220,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(iPr_def_11),iPr_def_11))),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1417,c_96510]) ).

tcf(c_102221,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(zero_zero_nat),iPr_def_11))),hAPP_nat_int(power_power_int(X1),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96510]) ).

tcf(c_102222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96510]) ).

tcf(c_102223,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96510]) ).

tcf(c_102224,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96510]) ).

tcf(c_102226,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_102223,c_78498]) ).

tcf(c_102245,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X3),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96626]) ).

tcf(c_102246,plain,
    ! [X0: $i,X1: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96626]) ).

tcf(c_102247,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96626]) ).

tcf(c_102249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X3),iPr_def_11)),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96626]) ).

tcf(c_102250,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96626]) ).

tcf(c_102254,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(iPr_def_11),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1417,c_96626]) ).

tcf(c_102255,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(zero_zero_nat),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96626]) ).

tcf(c_102256,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_102247,c_59636]) ).

tcf(c_102259,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_102246,c_78498]) ).

tcf(c_102310,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(demodulation,[status(thm)],[c_83536,c_253,c_90934]) ).

tcf(c_102315,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_574,c_102310]) ).

tcf(c_102316,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(min),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(min),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76397,c_102310]) ).

tcf(c_102317,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76393,c_102310]) ).

tcf(c_102318,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76395,c_102310]) ).

tcf(c_102319,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_76399,c_102310]) ).

tcf(c_102320,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(plus_plus_int(m),X2)))),
    inference(superposition,[status(thm)],[c_76401,c_102310]) ).

tcf(c_102321,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76402,c_102310]) ).

tcf(c_102322,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(s1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76403,c_102310]) ).

tcf(c_102323,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(s),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(s),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76404,c_102310]) ).

tcf(c_102324,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76405,c_102310]) ).

tcf(c_102325,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(sK9),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76406,c_102310]) ).

tcf(c_102326,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(sK10),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76407,c_102310]) ).

tcf(c_102327,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(sK11),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76408,c_102310]) ).

tcf(c_102328,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(sK13),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76409,c_102310]) ).

tcf(c_102329,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76410,c_102310]) ).

tcf(c_102330,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76411,c_102310]) ).

tcf(c_102331,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76412,c_102310]) ).

tcf(c_102332,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76413,c_102310]) ).

tcf(c_102333,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_76414,c_102310]) ).

tcf(c_102334,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76415,c_102310]) ).

tcf(c_102335,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_77366,c_102310]) ).

tcf(c_102336,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_78203,c_102310]) ).

tcf(c_102337,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79573,c_102310]) ).

tcf(c_102338,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79414,c_102310]) ).

tcf(c_102339,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79557,c_102310]) ).

tcf(c_102340,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79437,c_102310]) ).

tcf(c_102341,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79918,c_102310]) ).

tcf(c_102342,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_83504,c_102310]) ).

tcf(c_102343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80664,c_102310]) ).

tcf(c_102344,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80677,c_102310]) ).

tcf(c_102345,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80692,c_102310]) ).

tcf(c_102346,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80705,c_102310]) ).

tcf(c_102347,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_88502,c_102310]) ).

tcf(c_102348,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_88521,c_102310]) ).

tcf(c_102349,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_88558,c_102310]) ).

tcf(c_102350,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93551,c_102310]) ).

tcf(c_102351,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_93822,c_102310]) ).

tcf(c_102352,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_94573,c_102310]) ).

tcf(c_102353,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_94594,c_102310]) ).

tcf(c_102354,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_94672,c_102310]) ).

tcf(c_102355,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_94695,c_102310]) ).

tcf(c_102356,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95015,c_102310]) ).

tcf(c_102357,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95041,c_102310]) ).

tcf(c_102358,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95257,c_102310]) ).

tcf(c_102359,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95286,c_102310]) ).

tcf(c_102360,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95382,c_102310]) ).

tcf(c_102361,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_95414,c_102310]) ).

tcf(c_102362,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),pls))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),pls)))),
    inference(superposition,[status(thm)],[c_574,c_102310]) ).

tcf(c_102363,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),min))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),min)))),
    inference(superposition,[status(thm)],[c_76397,c_102310]) ).

tcf(c_102364,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),one_one_int)))),
    inference(superposition,[status(thm)],[c_76393,c_102310]) ).

tcf(c_102365,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),undefined_int(int))))),
    inference(superposition,[status(thm)],[c_76395,c_102310]) ).

tcf(c_102366,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1))))),
    inference(superposition,[status(thm)],[c_76399,c_102310]) ).

tcf(c_102367,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2))))),
    inference(superposition,[status(thm)],[c_76401,c_102310]) ).

tcf(c_102368,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),m)))),
    inference(superposition,[status(thm)],[c_76402,c_102310]) ).

tcf(c_102369,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s1))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),s1)))),
    inference(superposition,[status(thm)],[c_76403,c_102310]) ).

tcf(c_102370,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),s))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),s)))),
    inference(superposition,[status(thm)],[c_76404,c_102310]) ).

tcf(c_102371,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),t))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),t)))),
    inference(superposition,[status(thm)],[c_76405,c_102310]) ).

tcf(c_102372,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK9))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK9)))),
    inference(superposition,[status(thm)],[c_76406,c_102310]) ).

tcf(c_102373,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK10))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK10)))),
    inference(superposition,[status(thm)],[c_76407,c_102310]) ).

tcf(c_102374,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK11))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK11)))),
    inference(superposition,[status(thm)],[c_76408,c_102310]) ).

tcf(c_102375,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK13))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK13)))),
    inference(superposition,[status(thm)],[c_76409,c_102310]) ).

tcf(c_102376,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_14))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_76410,c_102310]) ).

tcf(c_102377,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_15))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_15)))),
    inference(superposition,[status(thm)],[c_76411,c_102310]) ).

tcf(c_102378,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_16))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_16)))),
    inference(superposition,[status(thm)],[c_76412,c_102310]) ).

tcf(c_102379,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_17))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_17)))),
    inference(superposition,[status(thm)],[c_76413,c_102310]) ).

tcf(c_102380,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),iPr_def_18))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_18)))),
    inference(superposition,[status(thm)],[c_76414,c_102310]) ).

tcf(c_102381,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_76415,c_102310]) ).

tcf(c_102382,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1))))),
    inference(superposition,[status(thm)],[c_77366,c_102310]) ).

tcf(c_102383,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))),
    inference(superposition,[status(thm)],[c_78203,c_102310]) ).

tcf(c_102384,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_79573,c_102310]) ).

tcf(c_102385,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_79414,c_102310]) ).

tcf(c_102386,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79557,c_102310]) ).

tcf(c_102387,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_79437,c_102310]) ).

tcf(c_102388,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X1))))),
    inference(superposition,[status(thm)],[c_79918,c_102310]) ).

tcf(c_102389,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_83504,c_102310]) ).

tcf(c_102390,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X1))))),
    inference(superposition,[status(thm)],[c_80664,c_102310]) ).

tcf(c_102391,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))))),
    inference(superposition,[status(thm)],[c_80677,c_102310]) ).

tcf(c_102392,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_80692,c_102310]) ).

tcf(c_102393,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_80705,c_102310]) ).

tcf(c_102394,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88502,c_102310]) ).

tcf(c_102395,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88521,c_102310]) ).

tcf(c_102396,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_88558,c_102310]) ).

tcf(c_102397,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_102310,c_65]) ).

tcf(c_102398,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0))))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,number_number_of_int(X1))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_102310,c_93890]) ).

tcf(c_102400,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))))),
    inference(superposition,[status(thm)],[c_102310,c_1042]) ).

tcf(c_102401,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),X2)) ),
    inference(superposition,[status(thm)],[c_102310,c_1027]) ).

tcf(c_102402,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),X2)) ),
    inference(superposition,[status(thm)],[c_102310,c_1024]) ).

tcf(c_102403,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))) = pls,
    inference(superposition,[status(thm)],[c_102310,c_92002]) ).

tcf(c_102404,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),X2),
    inference(superposition,[status(thm)],[c_102310,c_252]) ).

tcf(c_102405,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_102310,c_833]) ).

tcf(c_102407,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),number_number_of_int(X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_102310,c_253]) ).

tcf(c_102408,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_102310,c_76535]) ).

tcf(c_102409,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))),
    inference(superposition,[status(thm)],[c_102310,c_76498]) ).

tcf(c_102410,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))),
    inference(superposition,[status(thm)],[c_102310,c_1045]) ).

tcf(c_102411,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2))))) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X2))))),
    inference(superposition,[status(thm)],[c_102310,c_217]) ).

tcf(c_102413,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_102310,c_217]) ).

tcf(c_102415,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(m),X1))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))) ),
    inference(superposition,[status(thm)],[c_102310,c_1036]) ).

tcf(c_102416,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(m),X1))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_102310,c_833]) ).

tcf(c_102417,plain,
    ! [X0: $i,X1: $i] : is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),sK30(iPr_def_19),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_102310,c_90930]) ).

tcf(c_102420,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(light_normalisation,[status(thm)],[c_102368,c_79190]) ).

tcf(c_102421,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_102321,c_59637]) ).

tcf(c_102427,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(light_normalisation,[status(thm)],[c_102354,c_79557,c_90977,c_94573]) ).

tcf(c_102680,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X1),X2)),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_1039]) ).

tcf(c_102684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),X3))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X1),X2))) ),
    inference(superposition,[status(thm)],[c_252,c_1039]) ).

tcf(c_102685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),X3))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_217,c_1039]) ).

tcf(c_102688,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(X1),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_382,c_1039]) ).

tcf(c_102696,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_76995,c_1039]) ).

tcf(c_102697,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),undefined_int(int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_77063,c_1039]) ).

tcf(c_102698,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),twoSqu1241645765sum2sq(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_77069,c_1039]) ).

tcf(c_102699,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(X1),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),iPr_def_14)) ),
    inference(superposition,[status(thm)],[c_79150,c_1039]) ).

tcf(c_102700,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_83532,c_1039]) ).

tcf(c_102701,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_102310,c_1039]) ).

tcf(c_102702,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_88500,c_1039]) ).

tcf(c_102703,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_88519,c_1039]) ).

tcf(c_102704,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_88556,c_1039]) ).

tcf(c_102705,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) ),
    inference(superposition,[status(thm)],[c_96186,c_1039]) ).

tcf(c_102706,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_98014,c_1039]) ).

tcf(c_102707,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_98014,c_1039]) ).

tcf(c_102709,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(member_int(hAPP_int_int(times_times_int(X1),X2),hAPP_i1948725293t_bool(dvd_dvd_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1039,c_226]) ).

tcf(c_102710,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X1),X2),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1039,c_929]) ).

tcf(c_102711,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X0),X1) = pls )
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1039,c_1019]) ).

tcf(c_102712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(X2),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1039,c_1027]) ).

tcf(c_102713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(X2),X3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1039,c_1024]) ).

tcf(c_102825,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),X1) = one_one_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_674,c_1224]) ).

tcf(c_102830,plain,
    ! [X0: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( X0 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X0) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_82316,c_1224]) ).

tcf(c_102831,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X0) != one_one_nat ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_102830,c_78498]) ).

tcf(c_102880,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1364]) ).

tcf(c_102881,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ( number_number_of_nat(X0) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_1259,c_594]) ).

tcf(c_102891,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( X0 = X1 )
      | ( hAPP_nat_nat(div_mod_nat(X0),X1) = X0 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1693]) ).

tcf(c_102892,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1364]) ).

tcf(c_102893,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ( number_number_of_nat(X0) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_1259,c_594]) ).

tcf(c_102896,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X0 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1343]) ).

tcf(c_102897,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1344]) ).

tcf(c_102899,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X2),X1)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),X2))
      | ( hAPP_nat_nat(div_mod_nat(X0),X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1712]) ).

tcf(c_102900,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(iPr_def_10,X0)))
      | ( hAPP_nat_nat(iPr_def_10,X0) = one_one_nat ) ),
    inference(superposition,[status(thm)],[c_1259,c_77608]) ).

tcf(c_102901,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(iPr_def_10,X0)))
      | ( hAPP_nat_nat(iPr_def_10,X0) = X0 ) ),
    inference(superposition,[status(thm)],[c_1259,c_77614]) ).

tcf(c_102902,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),iPr_def_11))
    | ( one_one_nat = iPr_def_11 ) ),
    inference(superposition,[status(thm)],[c_1259,c_78984]) ).

tcf(c_102905,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),iPr_def_11)),
    inference(forward_subsumption_resolution,[status(thm)],[c_102902,c_78893]) ).

tcf(c_102906,plain,
    ! [X0: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(iPr_def_10,X0))),
    inference(forward_subsumption_resolution,[status(thm)],[c_102901,c_78756]) ).

tcf(c_103028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X3),X1))),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_11972,c_1262]) ).

tcf(c_103033,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1290,c_1262]) ).

tcf(c_103034,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1327,c_1262]) ).

tcf(c_103035,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_77538,c_1262]) ).

tcf(c_103036,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_77549,c_1262]) ).

tcf(c_103038,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),X0)) ),
    inference(superposition,[status(thm)],[c_78900,c_1262]) ).

tcf(c_103040,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) = hAPP_nat_nat(minus_minus_nat(X0),X2) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1262,c_1693]) ).

tcf(c_103041,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1262,c_1364]) ).

tcf(c_103043,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X0),X1))),
    inference(superposition,[status(thm)],[c_1262,c_1358]) ).

tcf(c_103045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X3)),X2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(div_mod_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1262,c_1712]) ).

tcf(c_103094,plain,
    hAPP_nat_nat(div_mod_nat(one_one_nat),iPr_def_11) = one_one_nat,
    inference(superposition,[status(thm)],[c_102905,c_1693]) ).

tcf(c_103119,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(X0,one_one_nat))
      | ~ sP4(one_one_nat,X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_103094,c_1711]) ).

tcf(c_103120,plain,
    ! [X0: $i] :
      ( sP4(one_one_nat,X0,iPr_def_11)
      | ~ hBOOL(hAPP_nat_bool(X0,one_one_nat)) ),
    inference(superposition,[status(thm)],[c_103094,c_1712]) ).

tcf(c_103132,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_96714,c_102310]) ).

tcf(c_103133,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_96714,c_101891]) ).

tcf(c_103134,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_96714,c_83534]) ).

tcf(c_103135,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),X1)),
    inference(superposition,[status(thm)],[c_96714,c_83532]) ).

tcf(c_103136,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),X1)),
    inference(superposition,[status(thm)],[c_96714,c_83524]) ).

tcf(c_103137,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96714,c_96186]) ).

tcf(c_103138,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_96714,c_90985]) ).

tcf(c_103139,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_96714,c_45898]) ).

tcf(c_103140,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_96714,c_45890]) ).

tcf(c_103141,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_96714,c_87033]) ).

tcf(c_103142,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_96714,c_86999]) ).

tcf(c_103143,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_96714,c_86619]) ).

tcf(c_103144,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_96714,c_86585]) ).

tcf(c_103145,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_96714,c_170]) ).

tcf(c_103146,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_96714,c_169]) ).

tcf(c_103147,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_96714,c_45982]) ).

tcf(c_103148,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_96714,c_45978]) ).

tcf(c_103149,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_96714,c_45914]) ).

tcf(c_103150,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_96714,c_629]) ).

tcf(c_103151,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_96714,c_628]) ).

tcf(c_103152,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_96714,c_879]) ).

tcf(c_103153,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_96714,c_388]) ).

tcf(c_103154,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_96714,c_79579]) ).

tcf(c_103155,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_96714,c_79562]) ).

tcf(c_103156,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_96714,c_382]) ).

tcf(c_103157,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) ),
    inference(superposition,[status(thm)],[c_96714,c_58]) ).

tcf(c_103158,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_96714,c_102310]) ).

tcf(c_103159,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_96714,c_83534]) ).

tcf(c_103160,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_96714,c_83532]) ).

tcf(c_103161,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_96714,c_83524]) ).

tcf(c_103162,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_96714,c_170]) ).

tcf(c_103163,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))) ),
    inference(superposition,[status(thm)],[c_96714,c_169]) ).

tcf(c_103164,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_96714,c_879]) ).

tcf(c_103165,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_96714,c_388]) ).

tcf(c_103166,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_96714,c_382]) ).

tcf(c_103167,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(m)),
    inference(superposition,[status(thm)],[c_96714,c_80692]) ).

tcf(c_103168,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_96714,c_80705]) ).

tcf(c_103169,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),m),
    inference(light_normalisation,[status(thm)],[c_103167,c_76402]) ).

tcf(c_103172,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_103168,c_76415]) ).

tcf(c_103304,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_99171]) ).

tcf(c_103305,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_253,c_99171]) ).

tcf(c_103307,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(X0),X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_217,c_99171]) ).

tcf(c_103309,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(pls)) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_1001,c_99171]) ).

tcf(c_103310,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(m)) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76855,c_99171]) ).

tcf(c_103311,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_99171,c_102310]) ).

tcf(c_103312,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_99171,c_101891]) ).

tcf(c_103313,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_99171,c_83534]) ).

tcf(c_103314,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),X1)),
    inference(superposition,[status(thm)],[c_99171,c_83532]) ).

tcf(c_103315,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),X1)),
    inference(superposition,[status(thm)],[c_99171,c_83524]) ).

tcf(c_103316,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_99171,c_96186]) ).

tcf(c_103317,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_99171,c_90985]) ).

tcf(c_103318,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_99171,c_45898]) ).

tcf(c_103319,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_99171,c_45890]) ).

tcf(c_103320,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_99171,c_87033]) ).

tcf(c_103321,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_99171,c_86999]) ).

tcf(c_103322,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_99171,c_86619]) ).

tcf(c_103323,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_99171,c_86585]) ).

tcf(c_103324,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_99171,c_170]) ).

tcf(c_103325,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_99171,c_169]) ).

tcf(c_103326,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_99171,c_45982]) ).

tcf(c_103327,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_99171,c_45978]) ).

tcf(c_103328,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_99171,c_45914]) ).

tcf(c_103329,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_99171,c_629]) ).

tcf(c_103330,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))) ),
    inference(superposition,[status(thm)],[c_99171,c_628]) ).

tcf(c_103331,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_99171,c_879]) ).

tcf(c_103332,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_99171,c_388]) ).

tcf(c_103333,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_99171,c_79579]) ).

tcf(c_103335,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),X1)),
    inference(superposition,[status(thm)],[c_99171,c_382]) ).

tcf(c_103336,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) ),
    inference(superposition,[status(thm)],[c_99171,c_58]) ).

tcf(c_103337,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))))),
    inference(superposition,[status(thm)],[c_99171,c_102310]) ).

tcf(c_103338,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_99171,c_83534]) ).

tcf(c_103339,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_99171,c_83532]) ).

tcf(c_103340,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_99171,c_83524]) ).

tcf(c_103341,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_99171,c_170]) ).

tcf(c_103342,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))) ),
    inference(superposition,[status(thm)],[c_99171,c_169]) ).

tcf(c_103343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_99171,c_879]) ).

tcf(c_103344,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_99171,c_388]) ).

tcf(c_103345,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_99171,c_382]) ).

tcf(c_103346,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_99171,c_79557]) ).

tcf(c_103347,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_99171,c_79437]) ).

tcf(c_103349,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_99171,c_99237]) ).

tcf(c_103351,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m)))),
    inference(superposition,[status(thm)],[c_99171,c_98014]) ).

tcf(c_103352,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))),
    inference(superposition,[status(thm)],[c_99171,c_98873]) ).

tcf(c_103353,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_99171,c_98014]) ).

tcf(c_103354,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_99171,c_98135]) ).

tcf(c_103355,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_99171,c_98875]) ).

tcf(c_103356,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_99171,c_99028]) ).

tcf(c_103357,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_99171,c_99033]) ).

tcf(c_103358,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(iPr_def_12,m))))),
    inference(superposition,[status(thm)],[c_99171,c_99036]) ).

tcf(c_103359,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),pls) = pls,
    inference(light_normalisation,[status(thm)],[c_103309,c_574]) ).

tcf(c_103360,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),one_one_int)))),
    inference(light_normalisation,[status(thm)],[c_103358,c_83540]) ).

tcf(c_103361,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(light_normalisation,[status(thm)],[c_103354,c_83504]) ).

tcf(c_103363,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),m) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_103310,c_76402]) ).

tcf(c_103364,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X1)))))),
    inference(light_normalisation,[status(thm)],[c_103357,c_92654]) ).

tcf(c_103367,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_103347,c_76415]) ).

tcf(c_103368,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),sK30(iPr_def_19)),
    inference(light_normalisation,[status(thm)],[c_103346,c_76415]) ).

tcf(c_103401,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(light_normalisation,[status(thm)],[c_103353,c_83504]) ).

tcf(c_103547,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_100498,c_102310]) ).

tcf(c_103548,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_100498,c_101891]) ).

tcf(c_103549,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_100498,c_83534]) ).

tcf(c_103550,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X1)),
    inference(superposition,[status(thm)],[c_100498,c_83532]) ).

tcf(c_103551,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X1)),
    inference(superposition,[status(thm)],[c_100498,c_83524]) ).

tcf(c_103552,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_96186]) ).

tcf(c_103553,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_100498,c_90985]) ).

tcf(c_103554,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_45898]) ).

tcf(c_103555,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_45890]) ).

tcf(c_103556,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_100498,c_87033]) ).

tcf(c_103557,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_86999]) ).

tcf(c_103558,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_100498,c_86619]) ).

tcf(c_103559,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_86585]) ).

tcf(c_103560,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_100498,c_170]) ).

tcf(c_103561,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)) ),
    inference(superposition,[status(thm)],[c_100498,c_169]) ).

tcf(c_103562,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),pls)) ),
    inference(superposition,[status(thm)],[c_100498,c_45982]) ).

tcf(c_103563,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),pls)) ),
    inference(superposition,[status(thm)],[c_100498,c_45978]) ).

tcf(c_103564,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_45914]) ).

tcf(c_103565,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_629]) ).

tcf(c_103566,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_628]) ).

tcf(c_103567,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_100498,c_879]) ).

tcf(c_103568,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_100498,c_388]) ).

tcf(c_103569,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_100498,c_79579]) ).

tcf(c_103570,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_79562]) ).

tcf(c_103571,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_100498,c_382]) ).

tcf(c_103572,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_100498,c_58]) ).

tcf(c_103573,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))))),
    inference(superposition,[status(thm)],[c_100498,c_102310]) ).

tcf(c_103574,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_100498,c_83534]) ).

tcf(c_103575,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_83532]) ).

tcf(c_103576,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_83524]) ).

tcf(c_103577,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_170]) ).

tcf(c_103578,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_100498,c_169]) ).

tcf(c_103579,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_879]) ).

tcf(c_103580,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_388]) ).

tcf(c_103581,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_382]) ).

tcf(c_103582,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(m)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = hAPP_int_int(minus_minus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_100498,c_80664]) ).

tcf(c_103583,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_100498,c_80677]) ).

tcf(c_103584,plain,
    hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_100498,c_96714]) ).

tcf(c_103585,plain,
    hAPP_int_int(minus_minus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_103582,c_76402]) ).

tcf(c_103588,plain,
    hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_103583,c_76415]) ).

tcf(c_103779,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_574,c_83537]) ).

tcf(c_103780,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(min),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(min),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76397,c_83537]) ).

tcf(c_103781,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76393,c_83537]) ).

tcf(c_103782,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(undefined_int(int)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76395,c_83537]) ).

tcf(c_103783,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_76399,c_83537]) ).

tcf(c_103784,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),hAPP_int_int(plus_plus_int(m),X2))),
    inference(superposition,[status(thm)],[c_76401,c_83537]) ).

tcf(c_103785,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76402,c_83537]) ).

tcf(c_103786,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s1),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(s1),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76403,c_83537]) ).

tcf(c_103787,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(s),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(s),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76404,c_83537]) ).

tcf(c_103788,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76405,c_83537]) ).

tcf(c_103789,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK9),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK9),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76406,c_83537]) ).

tcf(c_103790,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK10),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK10),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76407,c_83537]) ).

tcf(c_103791,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK11),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK11),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76408,c_83537]) ).

tcf(c_103792,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK13),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK13),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76409,c_83537]) ).

tcf(c_103793,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76410,c_83537]) ).

tcf(c_103794,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_15),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76411,c_83537]) ).

tcf(c_103795,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_16),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76412,c_83537]) ).

tcf(c_103796,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_17),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76413,c_83537]) ).

tcf(c_103797,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(iPr_def_18),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76414,c_83537]) ).

tcf(c_103798,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_76415,c_83537]) ).

tcf(c_103799,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_77366,c_83537]) ).

tcf(c_103800,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_78203,c_83537]) ).

tcf(c_103801,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79573,c_83537]) ).

tcf(c_103802,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79414,c_83537]) ).

tcf(c_103803,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79557,c_83537]) ).

tcf(c_103804,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_79437,c_83537]) ).

tcf(c_103806,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_83504,c_83537]) ).

tcf(c_103807,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80664,c_83537]) ).

tcf(c_103808,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80677,c_83537]) ).

tcf(c_103809,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80692,c_83537]) ).

tcf(c_103810,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_80705,c_83537]) ).

tcf(c_103811,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_88502,c_83537]) ).

tcf(c_103812,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_88521,c_83537]) ).

tcf(c_103813,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_88558,c_83537]) ).

tcf(c_103814,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_96714,c_83537]) ).

tcf(c_103815,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_99171,c_83537]) ).

tcf(c_103816,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_100498,c_83537]) ).

tcf(c_103817,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_83537]) ).

tcf(c_103818,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93822,c_83537]) ).

tcf(c_103819,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94573,c_83537]) ).

tcf(c_103820,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94594,c_83537]) ).

tcf(c_103821,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94672,c_83537]) ).

tcf(c_103822,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_94695,c_83537]) ).

tcf(c_103823,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95015,c_83537]) ).

tcf(c_103824,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95041,c_83537]) ).

tcf(c_103825,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95257,c_83537]) ).

tcf(c_103826,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95286,c_83537]) ).

tcf(c_103827,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95382,c_83537]) ).

tcf(c_103828,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95414,c_83537]) ).

tcf(c_103829,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),pls)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),pls))),
    inference(superposition,[status(thm)],[c_574,c_83537]) ).

tcf(c_103830,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),min)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),min))),
    inference(superposition,[status(thm)],[c_76397,c_83537]) ).

tcf(c_103831,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),one_one_int)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),one_one_int))),
    inference(superposition,[status(thm)],[c_76393,c_83537]) ).

tcf(c_103832,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),undefined_int(int))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),
    inference(superposition,[status(thm)],[c_76395,c_83537]) ).

tcf(c_103833,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1)))),
    inference(superposition,[status(thm)],[c_76399,c_83537]) ).

tcf(c_103834,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2)))),
    inference(superposition,[status(thm)],[c_76401,c_83537]) ).

tcf(c_103835,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),m)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),m))),
    inference(superposition,[status(thm)],[c_76402,c_83537]) ).

tcf(c_103836,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),s1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),s1))),
    inference(superposition,[status(thm)],[c_76403,c_83537]) ).

tcf(c_103837,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),s)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),s))),
    inference(superposition,[status(thm)],[c_76404,c_83537]) ).

tcf(c_103838,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),t)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),t))),
    inference(superposition,[status(thm)],[c_76405,c_83537]) ).

tcf(c_103839,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK9)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK9))),
    inference(superposition,[status(thm)],[c_76406,c_83537]) ).

tcf(c_103840,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK10)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK10))),
    inference(superposition,[status(thm)],[c_76407,c_83537]) ).

tcf(c_103841,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK11)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK11))),
    inference(superposition,[status(thm)],[c_76408,c_83537]) ).

tcf(c_103842,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK13)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK13))),
    inference(superposition,[status(thm)],[c_76409,c_83537]) ).

tcf(c_103843,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_14)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_14))),
    inference(superposition,[status(thm)],[c_76410,c_83537]) ).

tcf(c_103844,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_15)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_15))),
    inference(superposition,[status(thm)],[c_76411,c_83537]) ).

tcf(c_103845,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_16)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_16))),
    inference(superposition,[status(thm)],[c_76412,c_83537]) ).

tcf(c_103846,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_17)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_17))),
    inference(superposition,[status(thm)],[c_76413,c_83537]) ).

tcf(c_103847,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),iPr_def_18)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),iPr_def_18))),
    inference(superposition,[status(thm)],[c_76414,c_83537]) ).

tcf(c_103848,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_76415,c_83537]) ).

tcf(c_103849,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1)))),
    inference(superposition,[status(thm)],[c_77366,c_83537]) ).

tcf(c_103850,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78203,c_83537]) ).

tcf(c_103851,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79573,c_83537]) ).

tcf(c_103852,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_79414,c_83537]) ).

tcf(c_103853,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79557,c_83537]) ).

tcf(c_103854,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_79437,c_83537]) ).

tcf(c_103855,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79918,c_83537]) ).

tcf(c_103856,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_83504,c_83537]) ).

tcf(c_103857,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_80664,c_83537]) ).

tcf(c_103858,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1)))),
    inference(superposition,[status(thm)],[c_80677,c_83537]) ).

tcf(c_103859,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_80692,c_83537]) ).

tcf(c_103860,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_80705,c_83537]) ).

tcf(c_103861,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88502,c_83537]) ).

tcf(c_103862,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88521,c_83537]) ).

tcf(c_103863,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_88558,c_83537]) ).

tcf(c_103864,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_96714,c_83537]) ).

tcf(c_103865,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X1)))),
    inference(superposition,[status(thm)],[c_99171,c_83537]) ).

tcf(c_103866,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_100498,c_83537]) ).

tcf(c_103867,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0))))
      | ~ is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_83537,c_65]) ).

tcf(c_103868,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,number_number_of_int(X1))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_83537,c_93890]) ).

tcf(c_103870,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0))))),
    inference(superposition,[status(thm)],[c_83537,c_1042]) ).

tcf(c_103871,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),X2)) ),
    inference(superposition,[status(thm)],[c_83537,c_1027]) ).

tcf(c_103872,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),X2)) ),
    inference(superposition,[status(thm)],[c_83537,c_1024]) ).

tcf(c_103873,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),sK30(iPr_def_19)))),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))) = pls,
    inference(superposition,[status(thm)],[c_83537,c_92002]) ).

tcf(c_103874,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),X2)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),X2),
    inference(superposition,[status(thm)],[c_83537,c_252]) ).

tcf(c_103875,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))),hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_83537,c_833]) ).

tcf(c_103876,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))
      | ~ is_int(number_number_of_int(X0)) ),
    inference(superposition,[status(thm)],[c_83537,c_76863]) ).

tcf(c_103877,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0))),
    inference(superposition,[status(thm)],[c_83537,c_253]) ).

tcf(c_103878,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_83537,c_76535]) ).

tcf(c_103879,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_83537,c_76498]) ).

tcf(c_103880,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X0)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))),
    inference(superposition,[status(thm)],[c_83537,c_1045]) ).

tcf(c_103882,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X2)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_83537,c_1039]) ).

tcf(c_103883,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))) = hAPP_int_int(times_times_int(X1),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X2)))),
    inference(superposition,[status(thm)],[c_83537,c_217]) ).

tcf(c_103884,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(m),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_83537,c_1036]) ).

tcf(c_103885,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(m),X1)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_83537,c_833]) ).

tcf(c_103891,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_103835,c_79190]) ).

tcf(c_103892,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))),
    inference(light_normalisation,[status(thm)],[c_103785,c_59637]) ).

tcf(c_104221,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X0)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),
    inference(superposition,[status(thm)],[c_79342,c_1285]) ).

tcf(c_104224,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X0)),
    inference(superposition,[status(thm)],[c_1284,c_1285]) ).

tcf(c_104225,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(iPr_def_10,X0)),
    inference(superposition,[status(thm)],[c_77521,c_1285]) ).

tcf(c_104226,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0))) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),X0)),
    inference(superposition,[status(thm)],[c_94015,c_1285]) ).

tcf(c_104227,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1326,c_1285]) ).

tcf(c_104228,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat)) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(superposition,[status(thm)],[c_1325,c_1285]) ).

tcf(c_104229,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(iPr_def_10,X1)) = hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_59634,c_1285]) ).

tcf(c_104254,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X2) = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1285,c_1324]) ).

tcf(c_104255,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1285,c_1323]) ).

tcf(c_104256,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X2) = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != X1 ) ),
    inference(superposition,[status(thm)],[c_1285,c_1321]) ).

tcf(c_104258,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X0),X2))),
    inference(superposition,[status(thm)],[c_1285,c_1344]) ).

tcf(c_104259,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X1)),
    inference(superposition,[status(thm)],[c_1285,c_1343]) ).

tcf(c_104260,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2))) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1285,c_1327]) ).

tcf(c_104261,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X1) = hAPP_nat_nat(plus_plus_nat(X0),X2),
    inference(superposition,[status(thm)],[c_1285,c_1290]) ).

tcf(c_104262,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X0),X2)) = X1,
    inference(superposition,[status(thm)],[c_1285,c_1289]) ).

tcf(c_104265,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2)))),
    inference(superposition,[status(thm)],[c_1285,c_1375]) ).

tcf(c_104267,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)) = hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_1285,c_79342]) ).

tcf(c_104268,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),X3))),
    inference(superposition,[status(thm)],[c_1285,c_1285]) ).

tcf(c_104269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X2) = X3 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X1),X3) ) ),
    inference(superposition,[status(thm)],[c_1285,c_1287]) ).

tcf(c_104270,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)),
    inference(superposition,[status(thm)],[c_1285,c_1284]) ).

tcf(c_104271,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))),
    inference(superposition,[status(thm)],[c_1285,c_1373]) ).

tcf(c_104272,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1)) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1285,c_1326]) ).

tcf(c_104273,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X3 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X3),X2)) ) ),
    inference(superposition,[status(thm)],[c_1285,c_1288]) ).

tcf(c_104360,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X1),
    inference(superposition,[status(thm)],[c_79342,c_1286]) ).

tcf(c_104362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_1285,c_1286]) ).

tcf(c_104364,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2)),
    inference(superposition,[status(thm)],[c_1284,c_1286]) ).

tcf(c_104365,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),X1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(iPr_def_10,X0)),X1),
    inference(superposition,[status(thm)],[c_77521,c_1286]) ).

tcf(c_104366,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X0)),X2)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X0)),X2),
    inference(superposition,[status(thm)],[c_94015,c_1286]) ).

tcf(c_104369,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(iPr_def_10,X0)),X1) = hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_59634,c_1286]) ).

tcf(c_104370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_1286,c_1286]) ).

tcf(c_104373,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1286,c_1324]) ).

tcf(c_104374,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1286,c_1323]) ).

tcf(c_104375,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ),
    inference(superposition,[status(thm)],[c_1286,c_1321]) ).

tcf(c_104377,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X2)),
    inference(superposition,[status(thm)],[c_1286,c_1344]) ).

tcf(c_104378,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X0),X1))),
    inference(superposition,[status(thm)],[c_1286,c_1343]) ).

tcf(c_104379,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1286,c_1327]) ).

tcf(c_104380,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X0),X1)) = X2,
    inference(superposition,[status(thm)],[c_1286,c_1290]) ).

tcf(c_104381,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X2) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1286,c_1289]) ).

tcf(c_104384,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))),
    inference(superposition,[status(thm)],[c_1286,c_1375]) ).

tcf(c_104386,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X1))) = hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_1286,c_79342]) ).

tcf(c_104387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X3))),
    inference(superposition,[status(thm)],[c_1286,c_1285]) ).

tcf(c_104388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X2 = X3 )
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2) != hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X3)) ) ),
    inference(superposition,[status(thm)],[c_1286,c_1287]) ).

tcf(c_104389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),X3))),
    inference(superposition,[status(thm)],[c_1286,c_1285]) ).

tcf(c_104392,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))),
    inference(superposition,[status(thm)],[c_1286,c_1373]) ).

tcf(c_104393,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat)) = hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_1286,c_77521]) ).

tcf(c_104394,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),X1)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),hAPP_nat_nat(plus_plus_nat(X0),X1)),
    inference(superposition,[status(thm)],[c_1286,c_94015]) ).

tcf(c_104395,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat)) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1286,c_1325]) ).

tcf(c_104396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X3 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X3),X2) ) ),
    inference(superposition,[status(thm)],[c_1286,c_1288]) ).

tcf(c_104406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X3)) ) ),
    inference(light_normalisation,[status(thm)],[c_104388,c_104270]) ).

tcf(c_104441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)),
    inference(superposition,[status(thm)],[c_11972,c_1291]) ).

tcf(c_104442,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1244,c_1291]) ).

tcf(c_104444,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1246,c_1291]) ).

tcf(c_104445,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(minus_minus_nat(X0),X2),
    inference(superposition,[status(thm)],[c_1289,c_1291]) ).

tcf(c_104447,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X2),
    inference(superposition,[status(thm)],[c_1327,c_1291]) ).

tcf(c_104448,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(one_one_nat),X1),
    inference(superposition,[status(thm)],[c_77538,c_1291]) ).

tcf(c_104449,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(plus_plus_nat(one_one_nat),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_77549,c_1291]) ).

tcf(c_104450,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_77596,c_1291]) ).

tcf(c_104451,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(iPr_def_11),hAPP_nat_nat(plus_plus_nat(one_one_nat),X0)) = hAPP_nat_nat(minus_minus_nat(one_one_nat),X0),
    inference(superposition,[status(thm)],[c_78900,c_1291]) ).

tcf(c_104452,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(iPr_def_11),X0)) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X0),
    inference(superposition,[status(thm)],[c_78918,c_1291]) ).

tcf(c_104453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_1291,c_1291]) ).

tcf(c_104454,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
      | ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1291,c_1333]) ).

tcf(c_104456,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(minus_minus_nat(X0),X1))),
    inference(superposition,[status(thm)],[c_1291,c_1299]) ).

tcf(c_104457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)),
    inference(superposition,[status(thm)],[c_1291,c_11972]) ).

tcf(c_104458,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)),
    inference(superposition,[status(thm)],[c_1291,c_11972]) ).

tcf(c_104459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X3))),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1291,c_1262]) ).

tcf(c_104461,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X0),X1))) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1291,c_1246]) ).

tcf(c_104462,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1291,c_1327]) ).

tcf(c_104463,plain,
    ! [X0: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(plus_plus_nat(iPr_def_11),X0)) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_104452,c_1244]) ).

tcf(c_104466,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(one_one_nat),hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1))) = hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1),
    inference(light_normalisation,[status(thm)],[c_104450,c_104369]) ).

tcf(c_104467,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(iPr_def_10,X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(light_normalisation,[status(thm)],[c_104449,c_59634]) ).

tcf(c_104527,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),hAPP_nat_nat(plus_plus_nat(X0),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_79342,c_1292]) ).

tcf(c_104528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X3)) = hAPP_nat_nat(minus_minus_nat(X2),X3),
    inference(superposition,[status(thm)],[c_1286,c_1292]) ).

tcf(c_104529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X1),X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X3),
    inference(superposition,[status(thm)],[c_1285,c_1292]) ).

tcf(c_104533,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2),
    inference(superposition,[status(thm)],[c_94015,c_1292]) ).

tcf(c_104538,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)) = hAPP_nat_nat(minus_minus_nat(X1),X0),
    inference(superposition,[status(thm)],[c_79342,c_1292]) ).

tcf(c_104539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X3))) = hAPP_nat_nat(minus_minus_nat(X2),X3),
    inference(superposition,[status(thm)],[c_1286,c_1292]) ).

tcf(c_104540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),X3))) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_1285,c_1292]) ).

tcf(c_104543,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(iPr_def_10,X0)) = hAPP_nat_nat(minus_minus_nat(X1),one_one_nat),
    inference(superposition,[status(thm)],[c_77521,c_1292]) ).

tcf(c_104544,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),X0)) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0)),
    inference(superposition,[status(thm)],[c_94015,c_1292]) ).

tcf(c_104545,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0)),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1326,c_1292]) ).

tcf(c_104546,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0) = hAPP_nat_nat(minus_minus_nat(X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1325,c_1292]) ).

tcf(c_104548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X2)),X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3),
    inference(superposition,[status(thm)],[c_1292,c_1291]) ).

tcf(c_104549,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X2),X0)),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1292,c_1333]) ).

tcf(c_104551,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X0))),
    inference(superposition,[status(thm)],[c_1292,c_1299]) ).

tcf(c_104552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X0),X3))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X3)),X2),
    inference(superposition,[status(thm)],[c_1292,c_11972]) ).

tcf(c_104553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1292,c_1262]) ).

tcf(c_104562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X3))) = hAPP_nat_nat(minus_minus_nat(X2),X3),
    inference(light_normalisation,[status(thm)],[c_104539,c_104364]) ).

tcf(c_104623,plain,
    ! [X0: $i] : is_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(demodulation,[status(thm)],[c_99046,c_90827]) ).

tcf(c_104626,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(X0),hAPP_nat_nat(iPr_def_10,X0)) = X0,
    inference(superposition,[status(thm)],[c_102906,c_1693]) ).

tcf(c_104637,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),iPr_def_11)),
    inference(superposition,[status(thm)],[c_82861,c_103848]) ).

tcf(c_104638,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),
    inference(superposition,[status(thm)],[c_253,c_103848]) ).

tcf(c_104640,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_252,c_103848]) ).

tcf(c_104641,plain,
    hAPP_int_int(times_times_int(number_number_of_int(pls)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(pls),
    inference(superposition,[status(thm)],[c_1004,c_103848]) ).

tcf(c_104642,plain,
    hAPP_int_int(times_times_int(number_number_of_int(m)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_59637,c_103848]) ).

tcf(c_104643,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_103848,c_83537]) ).

tcf(c_104644,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_103848,c_101891]) ).

tcf(c_104645,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_103848,c_83534]) ).

tcf(c_104646,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X1)),
    inference(superposition,[status(thm)],[c_103848,c_83532]) ).

tcf(c_104647,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X1)),
    inference(superposition,[status(thm)],[c_103848,c_83524]) ).

tcf(c_104648,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_96186]) ).

tcf(c_104649,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_103848,c_90985]) ).

tcf(c_104650,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_45898]) ).

tcf(c_104651,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_45890]) ).

tcf(c_104652,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_103848,c_87033]) ).

tcf(c_104653,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_86999]) ).

tcf(c_104654,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_103848,c_86619]) ).

tcf(c_104655,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_86585]) ).

tcf(c_104656,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_103848,c_170]) ).

tcf(c_104657,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)) ),
    inference(superposition,[status(thm)],[c_103848,c_169]) ).

tcf(c_104658,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),pls)) ),
    inference(superposition,[status(thm)],[c_103848,c_45982]) ).

tcf(c_104659,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),pls)) ),
    inference(superposition,[status(thm)],[c_103848,c_45978]) ).

tcf(c_104660,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_45914]) ).

tcf(c_104661,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_629]) ).

tcf(c_104662,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_628]) ).

tcf(c_104663,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_103848,c_879]) ).

tcf(c_104664,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_103848,c_388]) ).

tcf(c_104665,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_103848,c_79579]) ).

tcf(c_104667,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X1)),
    inference(superposition,[status(thm)],[c_103848,c_382]) ).

tcf(c_104668,plain,
    ! [X0: $i] :
      ( is_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ~ is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_103848,c_58]) ).

tcf(c_104669,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_103848,c_83537]) ).

tcf(c_104670,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_103848,c_83534]) ).

tcf(c_104671,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_83532]) ).

tcf(c_104672,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_83524]) ).

tcf(c_104673,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_170]) ).

tcf(c_104674,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_103848,c_169]) ).

tcf(c_104675,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_879]) ).

tcf(c_104676,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_388]) ).

tcf(c_104677,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_382]) ).

tcf(c_104678,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_103848,c_79573]) ).

tcf(c_104679,plain,
    hAPP_int_int(times_times_int(number_number_of_int(sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_79414]) ).

tcf(c_104682,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(superposition,[status(thm)],[c_103848,c_99237]) ).

tcf(c_104684,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_103848,c_98014]) ).

tcf(c_104685,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_98873]) ).

tcf(c_104689,plain,
    hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_99171]) ).

tcf(c_104690,plain,
    hAPP_int_int(times_times_int(pls),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = pls,
    inference(light_normalisation,[status(thm)],[c_104641,c_574]) ).

tcf(c_104691,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),
    inference(light_normalisation,[status(thm)],[c_104682,c_79918]) ).

tcf(c_104692,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),m) = hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_104642,c_59637,c_76402,c_103363]) ).

tcf(c_104695,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),sK30(iPr_def_19)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_104679,c_76415,c_103368]) ).

tcf(c_104730,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(X0),m)))),
    inference(light_normalisation,[status(thm)],[c_104684,c_79918]) ).

tcf(c_104808,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),iPr_def_11)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_98912]) ).

tcf(c_104809,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)),X2) = pls,
    inference(superposition,[status(thm)],[c_253,c_98912]) ).

tcf(c_104811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_98912]) ).

tcf(c_104812,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_98912]) ).

tcf(c_104815,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_98912]) ).

tcf(c_104818,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79557,c_98912]) ).

tcf(c_104819,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79437,c_98912]) ).

tcf(c_104820,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99171,c_98912]) ).

tcf(c_104821,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_103848,c_98912]) ).

tcf(c_104822,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11))))),X0) = pls,
    inference(superposition,[status(thm)],[c_82861,c_98912]) ).

tcf(c_104827,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_1001,c_98912]) ).

tcf(c_104828,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76855,c_98912]) ).

tcf(c_104835,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m)),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_93890,c_98912]) ).

tcf(c_104836,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78930,c_98912]) ).

tcf(c_104837,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78938,c_98912]) ).

tcf(c_104838,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79190,c_98912]) ).

tcf(c_104839,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79161,c_98912]) ).

tcf(c_104840,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79901,c_98912]) ).

tcf(c_104841,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79904,c_98912]) ).

tcf(c_104843,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_85658,c_98912]) ).

tcf(c_104844,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88494,c_98912]) ).

tcf(c_104845,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88513,c_98912]) ).

tcf(c_104846,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88550,c_98912]) ).

tcf(c_104850,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_93551,c_98912]) ).

tcf(c_104862,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),pls))),
    inference(superposition,[status(thm)],[c_98912,c_76662]) ).

tcf(c_104864,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),pls),X0)),
    inference(superposition,[status(thm)],[c_98912,c_1698]) ).

tcf(c_104866,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_104827,c_574]) ).

tcf(c_104867,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))),X2) = pls,
    inference(light_normalisation,[status(thm)],[c_104809,c_98105]) ).

tcf(c_104941,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),iPr_def_11)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_99038]) ).

tcf(c_104942,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)),X2) = pls,
    inference(superposition,[status(thm)],[c_253,c_99038]) ).

tcf(c_104944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_99038]) ).

tcf(c_104945,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_99038]) ).

tcf(c_104948,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_99038]) ).

tcf(c_104951,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),m))),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79573,c_99038]) ).

tcf(c_104952,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79414,c_99038]) ).

tcf(c_104953,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99171,c_99038]) ).

tcf(c_104954,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),m)),iPr_def_11))))),X0) = pls,
    inference(superposition,[status(thm)],[c_82861,c_99038]) ).

tcf(c_104959,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),m)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_59637,c_99038]) ).

tcf(c_104963,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),m))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77148,c_99038]) ).

tcf(c_104964,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_13,iPr_def_14)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79190,c_99038]) ).

tcf(c_104966,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),pls))),
    inference(superposition,[status(thm)],[c_99038,c_76662]) ).

tcf(c_104968,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),pls),X0)),
    inference(superposition,[status(thm)],[c_99038,c_1698]) ).

tcf(c_104970,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))),X2) = pls,
    inference(light_normalisation,[status(thm)],[c_104942,c_98072]) ).

tcf(c_105046,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),hAPP_nat_nat(plus_plus_nat(X1),X0)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_79342,c_1293]) ).

tcf(c_105047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X3),
    inference(superposition,[status(thm)],[c_1286,c_1293]) ).

tcf(c_105048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(plus_plus_nat(X0),X2))) = hAPP_nat_nat(minus_minus_nat(X1),X3),
    inference(superposition,[status(thm)],[c_1285,c_1293]) ).

tcf(c_105052,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X0),X1))) = hAPP_nat_nat(minus_minus_nat(X1),X2),
    inference(superposition,[status(thm)],[c_94015,c_1293]) ).

tcf(c_105057,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_79342,c_1293]) ).

tcf(c_105058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X3),X1))) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_1286,c_1293]) ).

tcf(c_105059,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X3),X2))) = hAPP_nat_nat(minus_minus_nat(X0),X3),
    inference(superposition,[status(thm)],[c_1285,c_1293]) ).

tcf(c_105062,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),one_one_nat)),hAPP_nat_nat(iPr_def_10,X1)) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_77521,c_1293]) ).

tcf(c_105063,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X2)) = hAPP_nat_nat(minus_minus_nat(X0),X2),
    inference(superposition,[status(thm)],[c_94015,c_1293]) ).

tcf(c_105064,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X1) = hAPP_nat_nat(minus_minus_nat(X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1326,c_1293]) ).

tcf(c_105065,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat)),X1) = hAPP_nat_nat(minus_minus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1325,c_1293]) ).

tcf(c_105066,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(iPr_def_10,X1)) = hAPP_nat_nat(minus_minus_nat(X0),one_one_nat),
    inference(superposition,[status(thm)],[c_59634,c_1293]) ).

tcf(c_105067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X2),X1)),X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X3),
    inference(superposition,[status(thm)],[c_1293,c_1291]) ).

tcf(c_105068,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1293,c_1333]) ).

tcf(c_105070,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))),
    inference(superposition,[status(thm)],[c_1293,c_1299]) ).

tcf(c_105071,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X3),X1))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X3)),X2),
    inference(superposition,[status(thm)],[c_1293,c_11972]) ).

tcf(c_105072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X3)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1293,c_1262]) ).

tcf(c_105075,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(minus_minus_nat(X0),X0) = hAPP_nat_nat(minus_minus_nat(X1),X1),
    inference(superposition,[status(thm)],[c_1293,c_1292]) ).

tcf(c_105107,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),X1),
    inference(superposition,[status(thm)],[c_82316,c_1308]) ).

tcf(c_105110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X2)),X3)),
    inference(superposition,[status(thm)],[c_218,c_1308]) ).

tcf(c_105112,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(superposition,[status(thm)],[c_1309,c_1308]) ).

tcf(c_105115,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_nat(times_times_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1336,c_1308]) ).

tcf(c_105116,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(zero_zero_nat),X1)) = hAPP_nat_nat(times_times_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1337,c_1308]) ).

tcf(c_105117,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X1))) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X0),X1)),iPr_def_11),
    inference(superposition,[status(thm)],[c_1308,c_82316]) ).

tcf(c_105118,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X1)))))),
    inference(superposition,[status(thm)],[c_1308,c_1408]) ).

tcf(c_105120,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X1))))),
    inference(superposition,[status(thm)],[c_1308,c_1409]) ).

tcf(c_105121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1308,c_1038]) ).

tcf(c_105123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)),
    inference(superposition,[status(thm)],[c_1308,c_1308]) ).

tcf(c_105124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1308,c_1026]) ).

tcf(c_105125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1308,c_1023]) ).

tcf(c_105126,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_1308,c_1416]) ).

tcf(c_105127,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != one_one_nat ) ),
    inference(superposition,[status(thm)],[c_1308,c_1415]) ).

tcf(c_105128,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),hAPP_nat_nat(times_times_nat(X0),X1)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1308,c_1684]) ).

tcf(c_105132,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))),
    inference(superposition,[status(thm)],[c_1308,c_1044]) ).

tcf(c_105133,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X2),X3)) = hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X3))),
    inference(superposition,[status(thm)],[c_1308,c_218]) ).

tcf(c_105134,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3)) = hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X0),X3))),
    inference(superposition,[status(thm)],[c_1308,c_218]) ).

tcf(c_105136,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(times_times_nat(X1),X2))),X0),
    inference(superposition,[status(thm)],[c_1308,c_94015]) ).

tcf(c_105139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1308,c_1035]) ).

tcf(c_105140,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),one_one_nat)) = hAPP_nat_nat(times_times_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1308,c_1413]) ).

tcf(c_105141,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat)) = zero_zero_nat,
    inference(superposition,[status(thm)],[c_1308,c_1337]) ).

tcf(c_105142,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(X0),X1)))))),
    inference(superposition,[status(thm)],[c_1308,c_1408]) ).

tcf(c_105143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))),iPr_def_11))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96510]) ).

tcf(c_105152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96626]) ).

tcf(c_105225,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1291,c_1319]) ).

tcf(c_105226,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(X0),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_11972,c_1319]) ).

tcf(c_105230,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))) ),
    inference(superposition,[status(thm)],[c_1289,c_1319]) ).

tcf(c_105231,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1290,c_1319]) ).

tcf(c_105232,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X2))) ),
    inference(superposition,[status(thm)],[c_1292,c_1319]) ).

tcf(c_105233,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
    inference(superposition,[status(thm)],[c_1293,c_1319]) ).

tcf(c_105236,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(iPr_def_10,X0))) ),
    inference(superposition,[status(thm)],[c_77549,c_1319]) ).

tcf(c_105240,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),X0)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1319,c_1693]) ).

tcf(c_105241,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1319,c_1364]) ).

tcf(c_105266,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1320]) ).

tcf(c_105267,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),zero_zero_nat))
      | ( hAPP_nat_nat(minus_minus_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1259,c_1320]) ).

tcf(c_105270,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_1291,c_1320]) ).

tcf(c_105271,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_11972,c_1320]) ).

tcf(c_105272,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1244,c_1320]) ).

tcf(c_105274,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1246,c_1320]) ).

tcf(c_105275,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1289,c_1320]) ).

tcf(c_105276,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1290,c_1320]) ).

tcf(c_105277,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X2),X1)),hAPP_nat_nat(plus_plus_nat(X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1292,c_1320]) ).

tcf(c_105278,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1293,c_1320]) ).

tcf(c_105279,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1327,c_1320]) ).

tcf(c_105281,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(iPr_def_10,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_77549,c_1320]) ).

tcf(c_105282,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,X0)),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_77596,c_1320]) ).

tcf(c_105284,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),one_one_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_78918,c_1320]) ).

tcf(c_105375,plain,
    number_number_of_int(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
    inference(superposition,[status(thm)],[c_82935,c_78024]) ).

tcf(c_105377,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78024,c_83537]) ).

tcf(c_105378,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_78024,c_101891]) ).

tcf(c_105379,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X0)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78024,c_83534]) ).

tcf(c_105380,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0))),X1)),
    inference(superposition,[status(thm)],[c_78024,c_83532]) ).

tcf(c_105381,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0))),X1)),
    inference(superposition,[status(thm)],[c_78024,c_83524]) ).

tcf(c_105382,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78024,c_90985]) ).

tcf(c_105383,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(hAPP_int_int(iPr_def_12,X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_12,X0))) ),
    inference(superposition,[status(thm)],[c_78024,c_45898]) ).

tcf(c_105384,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(hAPP_int_int(iPr_def_12,X0))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),hAPP_int_int(iPr_def_12,X0))) ),
    inference(superposition,[status(thm)],[c_78024,c_45890]) ).

tcf(c_105389,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_78024,c_170]) ).

tcf(c_105390,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_78024,c_169]) ).

tcf(c_105391,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),pls)) ),
    inference(superposition,[status(thm)],[c_78024,c_45982]) ).

tcf(c_105392,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),pls)) ),
    inference(superposition,[status(thm)],[c_78024,c_45978]) ).

tcf(c_105393,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(iPr_def_12,X0))) ),
    inference(superposition,[status(thm)],[c_78024,c_45914]) ).

tcf(c_105396,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_12,X0)),X1)),
    inference(superposition,[status(thm)],[c_78024,c_879]) ).

tcf(c_105397,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),X1)),
    inference(superposition,[status(thm)],[c_78024,c_388]) ).

tcf(c_105400,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),X1)),
    inference(superposition,[status(thm)],[c_78024,c_382]) ).

tcf(c_105402,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1)))),
    inference(superposition,[status(thm)],[c_78024,c_83537]) ).

tcf(c_105403,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1)))),
    inference(superposition,[status(thm)],[c_78024,c_83534]) ).

tcf(c_105404,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_83532]) ).

tcf(c_105405,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_83524]) ).

tcf(c_105406,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_12,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1))) ),
    inference(superposition,[status(thm)],[c_78024,c_170]) ).

tcf(c_105407,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(iPr_def_12,X1))) ),
    inference(superposition,[status(thm)],[c_78024,c_169]) ).

tcf(c_105408,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_879]) ).

tcf(c_105409,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_388]) ).

tcf(c_105410,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_382]) ).

tcf(c_105411,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,X1)) = number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1))),
    inference(light_normalisation,[status(thm)],[c_105409,c_92944]) ).

tcf(c_105412,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X1))),
    inference(light_normalisation,[status(thm)],[c_105397,c_92633]) ).

tcf(c_105431,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),number_number_of_int(X0)))),
    inference(demodulation,[status(thm)],[c_98881,c_105400]) ).

tcf(c_105432,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_12,m)))),
    inference(demodulation,[status(thm)],[c_99036,c_105410]) ).

tcf(c_105456,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK27(X0,t)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK27(X0,t)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78042,c_83537]) ).

tcf(c_105457,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK27(X0,t)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_78042,c_101891]) ).

tcf(c_105458,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK27(X0,t)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK27(X0,t)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78042,c_83534]) ).

tcf(c_105459,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK27(X0,t))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK27(X0,t))),X1)),
    inference(superposition,[status(thm)],[c_78042,c_83532]) ).

tcf(c_105460,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK27(X0,t))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK27(X0,t))),X1)),
    inference(superposition,[status(thm)],[c_78042,c_83524]) ).

tcf(c_105461,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK27(X0,t)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78042,c_90985]) ).

tcf(c_105462,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK27(X0,t))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK27(X0,t))) ),
    inference(superposition,[status(thm)],[c_78042,c_45898]) ).

tcf(c_105463,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK27(X0,t))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK27(X0,t))) ),
    inference(superposition,[status(thm)],[c_78042,c_45890]) ).

tcf(c_105468,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,t)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,t)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_78042,c_170]) ).

tcf(c_105469,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,t)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,t)),X1)) ),
    inference(superposition,[status(thm)],[c_78042,c_169]) ).

tcf(c_105470,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK27(X0,t)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,t)),pls)) ),
    inference(superposition,[status(thm)],[c_78042,c_45982]) ).

tcf(c_105471,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK27(X0,t)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK27(X0,t)),pls)) ),
    inference(superposition,[status(thm)],[c_78042,c_45978]) ).

tcf(c_105472,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK27(X0,t)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK27(X0,t))) ),
    inference(superposition,[status(thm)],[c_78042,c_45914]) ).

tcf(c_105475,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK27(X0,t)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK27(X0,t)),X1)),
    inference(superposition,[status(thm)],[c_78042,c_879]) ).

tcf(c_105476,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK27(X0,t)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK27(X0,t)),X1)),
    inference(superposition,[status(thm)],[c_78042,c_388]) ).

tcf(c_105479,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK27(X0,t)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(sK27(X0,t)),X1)),
    inference(superposition,[status(thm)],[c_78042,c_382]) ).

tcf(c_105481,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK27(X1,t))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK27(X1,t)))),
    inference(superposition,[status(thm)],[c_78042,c_83537]) ).

tcf(c_105482,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK27(X1,t))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK27(X1,t)))),
    inference(superposition,[status(thm)],[c_78042,c_83534]) ).

tcf(c_105483,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK27(X1,t)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_83532]) ).

tcf(c_105484,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK27(X1,t)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_83524]) ).

tcf(c_105485,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK27(X1,t)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK27(X1,t))) ),
    inference(superposition,[status(thm)],[c_78042,c_170]) ).

tcf(c_105486,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK27(X1,t)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK27(X1,t))) ),
    inference(superposition,[status(thm)],[c_78042,c_169]) ).

tcf(c_105487,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK27(X1,t)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_879]) ).

tcf(c_105488,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK27(X1,t)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_388]) ).

tcf(c_105489,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK27(X1,t)) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_382]) ).

tcf(c_105563,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK27(X0,one_one_int)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(times_times_int(sK27(X0,one_one_int)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78056,c_83537]) ).

tcf(c_105564,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK27(X0,one_one_int)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),hAPP_nat_nat(times_times_nat(iPr_def_11),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_78056,c_101891]) ).

tcf(c_105565,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK27(X0,one_one_int)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))) = number_number_of_int(hAPP_int_int(minus_minus_int(sK27(X0,one_one_int)),hAPP_int_int(plus_plus_int(m),X1))),
    inference(superposition,[status(thm)],[c_78056,c_83534]) ).

tcf(c_105566,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int))),X1)),
    inference(superposition,[status(thm)],[c_78056,c_83532]) ).

tcf(c_105567,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int))),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int))),X1)),
    inference(superposition,[status(thm)],[c_78056,c_83524]) ).

tcf(c_105568,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK27(X0,one_one_int)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_78056,c_90985]) ).

tcf(c_105569,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(sK27(X0,one_one_int))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK27(X0,one_one_int))) ),
    inference(superposition,[status(thm)],[c_78056,c_45898]) ).

tcf(c_105570,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK27(X0,one_one_int))),one_one_real))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),sK27(X0,one_one_int))) ),
    inference(superposition,[status(thm)],[c_78056,c_45890]) ).

tcf(c_105575,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,one_one_int)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_78056,c_170]) ).

tcf(c_105576,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,one_one_int)),number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,one_one_int)),X1)) ),
    inference(superposition,[status(thm)],[c_78056,c_169]) ).

tcf(c_105577,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),sK27(X0,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK27(X0,one_one_int)),pls)) ),
    inference(superposition,[status(thm)],[c_78056,c_45982]) ).

tcf(c_105578,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK27(X0,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK27(X0,one_one_int)),pls)) ),
    inference(superposition,[status(thm)],[c_78056,c_45978]) ).

tcf(c_105579,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),sK27(X0,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK27(X0,one_one_int))) ),
    inference(superposition,[status(thm)],[c_78056,c_45914]) ).

tcf(c_105582,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(sK27(X0,one_one_int)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(minus_minus_int(sK27(X0,one_one_int)),X1)),
    inference(superposition,[status(thm)],[c_78056,c_879]) ).

tcf(c_105583,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK27(X0,one_one_int)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(sK27(X0,one_one_int)),X1)),
    inference(superposition,[status(thm)],[c_78056,c_388]) ).

tcf(c_105586,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK27(X0,one_one_int)),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(times_times_int(sK27(X0,one_one_int)),X1)),
    inference(superposition,[status(thm)],[c_78056,c_382]) ).

tcf(c_105588,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int))) = number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int)))),
    inference(superposition,[status(thm)],[c_78056,c_83537]) ).

tcf(c_105589,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int))) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int)))),
    inference(superposition,[status(thm)],[c_78056,c_83534]) ).

tcf(c_105590,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK27(X1,one_one_int)) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_83532]) ).

tcf(c_105591,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK27(X1,one_one_int)) = number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_83524]) ).

tcf(c_105592,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK27(X1,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK27(X1,one_one_int))) ),
    inference(superposition,[status(thm)],[c_78056,c_170]) ).

tcf(c_105593,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),sK27(X1,one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK27(X1,one_one_int))) ),
    inference(superposition,[status(thm)],[c_78056,c_169]) ).

tcf(c_105594,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK27(X1,one_one_int)) = number_number_of_int(hAPP_int_int(minus_minus_int(X0),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_879]) ).

tcf(c_105595,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(X0)),sK27(X1,one_one_int)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_388]) ).

tcf(c_105596,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),sK27(X1,one_one_int)) = number_number_of_int(hAPP_int_int(times_times_int(X0),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_382]) ).

tcf(c_105678,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK26(iPr_def_14)))
      | ~ hBOOL(hAPP_int_bool(zcong(sK26(iPr_def_14),pls),X0)) ),
    inference(superposition,[status(thm)],[c_78197,c_897]) ).

tcf(c_105679,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(sK26(iPr_def_14),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK26(iPr_def_14))) ),
    inference(superposition,[status(thm)],[c_78197,c_896]) ).

tcf(c_105699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X2),X3)),iPr_def_11)) != iPr_def_18,
    inference(demodulation,[status(thm)],[c_96093,c_91969]) ).

tcf(c_105704,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96506]) ).

tcf(c_105712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))),X3))),hAPP_nat_int(power_power_int(X4),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96506]) ).

tcf(c_105720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X2),iPr_def_11)),X3)))),hAPP_nat_int(power_power_int(X4),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96506]) ).

tcf(c_105724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11)))))),hAPP_nat_int(power_power_int(X5),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96506]) ).

tcf(c_105727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),zero_zero_nat)))),hAPP_nat_int(power_power_int(X3),iPr_def_11)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96506]) ).

tcf(c_105728,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),hAPP_nat_int(power_power_int(X4),hAPP_nat_nat(times_times_nat(X5),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_676,c_96506]) ).

tcf(c_105729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96506]) ).

tcf(c_105730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),one_one_int) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96506]) ).

tcf(c_105732,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),pls) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_105729,c_78498]) ).

tcf(c_105745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96521]) ).

tcf(c_105753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),X2))),hAPP_nat_int(power_power_int(X3),hAPP_nat_nat(times_times_nat(X4),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96521]) ).

tcf(c_105760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),zero_zero_nat))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96521]) ).

tcf(c_105766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),hAPP_nat_nat(times_times_nat(X4),hAPP_nat_nat(times_times_nat(X5),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96521]) ).

tcf(c_105769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),hAPP_nat_int(power_power_int(X3),zero_zero_nat)) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96521]) ).

tcf(c_105836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),zero_zero_nat)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96605]) ).

tcf(c_105838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96605]) ).

tcf(c_105846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X3),iPr_def_11)),X4))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96605]) ).

tcf(c_105850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),hAPP_nat_nat(times_times_nat(X5),iPr_def_11))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96605]) ).

tcf(c_105853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),hAPP_nat_int(power_power_int(X2),hAPP_nat_nat(times_times_nat(X3),zero_zero_nat))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96605]) ).

tcf(c_105863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( zero_zero_nat = iPr_def_11 )
      | ( hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96622]) ).

tcf(c_105864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_673,c_96622]) ).

tcf(c_105867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) = zero_zero_nat )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),pls) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_491,c_96622]) ).

tcf(c_105875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))),X4))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96622]) ).

tcf(c_105883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X3),iPr_def_11)),X4)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1309,c_96622]) ).

tcf(c_105887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),hAPP_nat_nat(times_times_nat(X4),hAPP_nat_nat(times_times_nat(X5),iPr_def_11)))))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1308,c_96622]) ).

tcf(c_105890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),zero_zero_nat)))) != iPr_def_18,
    inference(superposition,[status(thm)],[c_1336,c_96622]) ).

tcf(c_105891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(iPr_def_12,hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18,
    inference(light_normalisation,[status(thm)],[c_105864,c_59636]) ).

tcf(c_105894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18,
    inference(forward_subsumption_resolution,[status(thm)],[c_105863,c_78498]) ).

tcf(c_105901,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_95608]) ).

tcf(c_105902,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_95608]) ).

tcf(c_105903,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_95608]) ).

tcf(c_105904,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_95608]) ).

tcf(c_105906,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_95608]) ).

tcf(c_105907,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_95608]) ).

tcf(c_105909,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_95608]) ).

tcf(c_105910,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_95608]) ).

tcf(c_105911,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_95608]) ).

tcf(c_105912,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_95608]) ).

tcf(c_105913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_95608]) ).

tcf(c_105914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_95608]) ).

tcf(c_105915,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_95608]) ).

tcf(c_105916,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_95608]) ).

tcf(c_105917,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_95608]) ).

tcf(c_105918,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_95608]) ).

tcf(c_105919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_95608]) ).

tcf(c_105920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_95608]) ).

tcf(c_105921,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_95608]) ).

tcf(c_105922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_95608]) ).

tcf(c_105923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_95608]) ).

tcf(c_105924,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_95608]) ).

tcf(c_105925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_95608]) ).

tcf(c_105926,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_95608]) ).

tcf(c_105927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_95608]) ).

tcf(c_105928,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_95608]) ).

tcf(c_105929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_95608]) ).

tcf(c_105930,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_95608]) ).

tcf(c_105931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_95608]) ).

tcf(c_105932,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_95608]) ).

tcf(c_105933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_95608]) ).

tcf(c_105934,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_95608]) ).

tcf(c_105935,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_95608]) ).

tcf(c_105938,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_92656]) ).

tcf(c_105939,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_95608,c_255]) ).

tcf(c_105941,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95608,c_256]) ).

tcf(c_105943,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95608,c_83532]) ).

tcf(c_105944,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_95608,c_83524]) ).

tcf(c_105945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_95608]) ).

tcf(c_105949,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95608,c_98014]) ).

tcf(c_105950,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_95414]) ).

tcf(c_105951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_95286]) ).

tcf(c_105952,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_95041]) ).

tcf(c_105953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_94695]) ).

tcf(c_105954,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_94594]) ).

tcf(c_105955,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_93822]) ).

tcf(c_105956,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_93551]) ).

tcf(c_105957,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95608,c_79918]) ).

tcf(c_105958,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95608,c_83537]) ).

tcf(c_105959,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95608,c_83534]) ).

tcf(c_105964,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95608,c_96186]) ).

tcf(c_105965,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_105906,c_59636]) ).

tcf(c_105966,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_105901,c_79190]) ).

tcf(c_105967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_105957,c_76415]) ).

tcf(c_105968,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_105909,c_76855,c_93903]) ).

tcf(c_105972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_105949,c_79573]) ).

tcf(c_106057,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(m),one_one_int)) = m,
    inference(superposition,[status(thm)],[c_59636,c_83594]) ).

tcf(c_106060,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_92656]) ).

tcf(c_106061,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),X0)),X1)) = hAPP_int_int(plus_plus_int(m),X1),
    inference(superposition,[status(thm)],[c_83594,c_255]) ).

tcf(c_106063,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(m),X0))) = hAPP_int_int(plus_plus_int(X1),m),
    inference(superposition,[status(thm)],[c_83594,c_256]) ).

tcf(c_106065,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))) = m,
    inference(superposition,[status(thm)],[c_83594,c_255]) ).

tcf(c_106066,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_95608]) ).

tcf(c_106067,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(m),X0))))),
    inference(superposition,[status(thm)],[c_83594,c_99237]) ).

tcf(c_106068,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(m),iPr_def_11))),
    inference(superposition,[status(thm)],[c_83594,c_99891]) ).

tcf(c_106070,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0))),
    inference(superposition,[status(thm)],[c_83594,c_98014]) ).

tcf(c_106071,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_95414]) ).

tcf(c_106072,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_95286]) ).

tcf(c_106073,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_95041]) ).

tcf(c_106074,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_94695]) ).

tcf(c_106075,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_94594]) ).

tcf(c_106076,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_93822]) ).

tcf(c_106077,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_93551]) ).

tcf(c_106078,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(m),m))) = number_number_of_int(m),
    inference(superposition,[status(thm)],[c_83594,c_79918]) ).

tcf(c_106082,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X0),m),
    inference(superposition,[status(thm)],[c_83594,c_92625]) ).

tcf(c_106083,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_83594,c_98912]) ).

tcf(c_106085,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(m),X1))))),
    inference(superposition,[status(thm)],[c_83594,c_98875]) ).

tcf(c_106088,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(m),m))) = m,
    inference(light_normalisation,[status(thm)],[c_106078,c_76402]) ).

tcf(c_106090,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,X1))))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_106083,c_59637]) ).

tcf(c_106091,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_106070,c_59637,c_77366]) ).

tcf(c_106168,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),iPr_def_11) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_82316,c_1338]) ).

tcf(c_106170,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1308,c_1338]) ).

tcf(c_106171,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X2) = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_218,c_1338]) ).

tcf(c_106193,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_79342,c_1347]) ).

tcf(c_106194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1286,c_1347]) ).

tcf(c_106195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1285,c_1347]) ).

tcf(c_106198,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(iPr_def_10,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_77521,c_1347]) ).

tcf(c_106199,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_94015,c_1347]) ).

tcf(c_106202,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(iPr_def_10,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_59634,c_1347]) ).

tcf(c_106203,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1347,c_1693]) ).

tcf(c_106204,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1347,c_1364]) ).

tcf(c_106206,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)),X0)),
    inference(superposition,[status(thm)],[c_1347,c_1343]) ).

tcf(c_106209,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1))),X0)),
    inference(superposition,[status(thm)],[c_1347,c_77614]) ).

tcf(c_106242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X3),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1286,c_1348]) ).

tcf(c_106243,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X3),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1285,c_1348]) ).

tcf(c_106247,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_94015,c_1348]) ).

tcf(c_106251,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1348,c_1693]) ).

tcf(c_106252,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1348,c_1364]) ).

tcf(c_106254,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)),X1)),
    inference(superposition,[status(thm)],[c_1348,c_1343]) ).

tcf(c_106257,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1))),X1)),
    inference(superposition,[status(thm)],[c_1348,c_77614]) ).

tcf(c_106258,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X0)),
    inference(light_normalisation,[status(thm)],[c_106254,c_104364]) ).

tcf(c_106334,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X3),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1348,c_1352]) ).

tcf(c_106335,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1352]) ).

tcf(c_106336,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1347,c_1352]) ).

tcf(c_106337,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK35(X2,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1577,c_1352]) ).

tcf(c_106338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(div_mod_nat(X0),X3)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) ),
    inference(superposition,[status(thm)],[c_1711,c_1352]) ).

tcf(c_106339,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1)))),
    inference(superposition,[status(thm)],[c_102906,c_1352]) ).

tcf(c_106341,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79342,c_1352]) ).

tcf(c_106342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1286,c_1352]) ).

tcf(c_106343,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1285,c_1352]) ).

tcf(c_106347,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_94015,c_1352]) ).

tcf(c_106368,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK35(X2,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_106337,c_1317]) ).

tcf(c_106377,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(sK26(iPr_def_14)),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(sK26(iPr_def_14)),X0),
    inference(superposition,[status(thm)],[c_78198,c_676]) ).

tcf(c_106379,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(iPr_def_14)),sK26(iPr_def_14)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_78198,c_805]) ).

tcf(c_106382,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK26(iPr_def_14)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78200,c_92656]) ).

tcf(c_106383,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),X0)) = hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),X0),
    inference(superposition,[status(thm)],[c_78200,c_255]) ).

tcf(c_106385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),sK26(iPr_def_14))) = hAPP_int_int(plus_plus_int(X0),sK26(iPr_def_14)),
    inference(superposition,[status(thm)],[c_78200,c_256]) ).

tcf(c_106409,plain,
    hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),sK26(iPr_def_14)) = hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),sK26(iPr_def_14)),
    inference(superposition,[status(thm)],[c_78201,c_93890]) ).

tcf(c_106410,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK26(iPr_def_14)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78201,c_1042]) ).

tcf(c_106413,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))),sK26(iPr_def_14)) = pls,
    inference(superposition,[status(thm)],[c_78201,c_92002]) ).

tcf(c_106414,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(sK26(iPr_def_14)),X0)) = hAPP_int_int(times_times_int(sK26(iPr_def_14)),X0),
    inference(superposition,[status(thm)],[c_78201,c_252]) ).

tcf(c_106415,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK26(iPr_def_14),hAPP_int_int(times_times_int(X0),sK26(iPr_def_14))),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78201,c_833]) ).

tcf(c_106417,plain,
    hBOOL(member_int(sK26(iPr_def_14),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_78201,c_76535]) ).

tcf(c_106418,plain,
    hBOOL(member_int(sK26(iPr_def_14),hAPP_i1948725293t_bool(dvd_dvd_int,sK26(iPr_def_14)))),
    inference(superposition,[status(thm)],[c_78201,c_76498]) ).

tcf(c_106419,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78201,c_1045]) ).

tcf(c_106421,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),sK26(iPr_def_14)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_78201,c_1039]) ).

tcf(c_106422,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),sK26(iPr_def_14))) = hAPP_int_int(times_times_int(X0),sK26(iPr_def_14)),
    inference(superposition,[status(thm)],[c_78201,c_217]) ).

tcf(c_106424,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),sK26(iPr_def_14)),sK26(iPr_def_14)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78201,c_833]) ).

tcf(c_106427,plain,
    hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),sK26(iPr_def_14)) = hAPP_int_int(times_times_int(iPr_def_14),sK26(iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_106409,c_59638]) ).

tcf(c_106434,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_92656]) ).

tcf(c_106435,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_95573,c_255]) ).

tcf(c_106437,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95573,c_256]) ).

tcf(c_106439,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95573,c_83532]) ).

tcf(c_106440,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_95573,c_83524]) ).

tcf(c_106441,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_95608]) ).

tcf(c_106445,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_95573,c_98014]) ).

tcf(c_106446,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_95414]) ).

tcf(c_106447,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_95286]) ).

tcf(c_106448,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_95041]) ).

tcf(c_106449,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_94695]) ).

tcf(c_106450,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_94594]) ).

tcf(c_106451,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_93822]) ).

tcf(c_106452,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_93551]) ).

tcf(c_106453,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95573,c_79918]) ).

tcf(c_106454,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95573,c_83537]) ).

tcf(c_106455,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95573,c_83534]) ).

tcf(c_106460,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_95573,c_96186]) ).

tcf(c_106467,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_106445,c_79573]) ).

tcf(c_106496,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(demodulation,[status(thm)],[c_98919,c_253,c_79573]) ).

tcf(c_106498,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_79557,c_106496]) ).

tcf(c_106500,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_99171,c_106496]) ).

tcf(c_106501,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_106496]) ).

tcf(c_106502,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_106496]) ).

tcf(c_106503,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_253,c_106496]) ).

tcf(c_106505,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_217,c_106496]) ).

tcf(c_106507,plain,
    hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(pls))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_106496]) ).

tcf(c_106508,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76855,c_106496]) ).

tcf(c_106509,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_83532,c_106496]) ).

tcf(c_106510,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),X1))),
    inference(superposition,[status(thm)],[c_257,c_106496]) ).

tcf(c_106512,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,m)),X0))),
    inference(superposition,[status(thm)],[c_76874,c_106496]) ).

tcf(c_106513,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))),X2))),
    inference(superposition,[status(thm)],[c_256,c_106496]) ).

tcf(c_106515,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1))),
    inference(superposition,[status(thm)],[c_93890,c_106496]) ).

tcf(c_106516,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1))),
    inference(superposition,[status(thm)],[c_78930,c_106496]) ).

tcf(c_106517,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))),
    inference(superposition,[status(thm)],[c_78938,c_106496]) ).

tcf(c_106518,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))),
    inference(superposition,[status(thm)],[c_79190,c_106496]) ).

tcf(c_106519,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1))),
    inference(superposition,[status(thm)],[c_79161,c_106496]) ).

tcf(c_106520,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1))),
    inference(superposition,[status(thm)],[c_79901,c_106496]) ).

tcf(c_106521,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79904,c_106496]) ).

tcf(c_106522,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(m),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0))),
    inference(superposition,[status(thm)],[c_83594,c_106496]) ).

tcf(c_106524,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_85658,c_106496]) ).

tcf(c_106525,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88494,c_106496]) ).

tcf(c_106526,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88513,c_106496]) ).

tcf(c_106527,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88550,c_106496]) ).

tcf(c_106529,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)),X1))),
    inference(superposition,[status(thm)],[c_92625,c_106496]) ).

tcf(c_106530,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_92936,c_106496]) ).

tcf(c_106531,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93551,c_106496]) ).

tcf(c_106546,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_106496,c_93890]) ).

tcf(c_106547,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_106496,c_1042]) ).

tcf(c_106549,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) ),
    inference(superposition,[status(thm)],[c_106496,c_1024]) ).

tcf(c_106550,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = pls,
    inference(superposition,[status(thm)],[c_106496,c_92002]) ).

tcf(c_106551,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2),
    inference(superposition,[status(thm)],[c_106496,c_252]) ).

tcf(c_106552,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_int_int(times_times_int(X2),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_106496,c_833]) ).

tcf(c_106555,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))),
    inference(superposition,[status(thm)],[c_106496,c_76498]) ).

tcf(c_106559,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_106496,c_217]) ).

tcf(c_106560,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) ),
    inference(superposition,[status(thm)],[c_106496,c_1036]) ).

tcf(c_106561,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),
    inference(superposition,[status(thm)],[c_106496,c_833]) ).

tcf(c_106568,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),pls),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_106496,c_84092]) ).

tcf(c_106569,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),pls))),
    inference(superposition,[status(thm)],[c_106496,c_84084]) ).

tcf(c_106570,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) = pls,
    inference(superposition,[status(thm)],[c_106496,c_83484]) ).

tcf(c_106571,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_106496,c_79573]) ).

tcf(c_106572,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_106496,c_79414]) ).

tcf(c_106583,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_106531,c_79573]) ).

tcf(c_106584,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_106518,c_99243]) ).

tcf(c_106585,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_106508,c_102421,c_103892]) ).

tcf(c_106586,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(light_normalisation,[status(thm)],[c_106509,c_106496]) ).

tcf(c_106587,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_106498,c_79918]) ).

tcf(c_106588,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_106515,c_93903,c_99172]) ).

tcf(c_106593,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m)))),X2)),
    inference(light_normalisation,[status(thm)],[c_106551,c_98105]) ).

tcf(c_106594,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_106501,c_79918]) ).

tcf(c_106595,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_106525,c_88957]) ).

tcf(c_106596,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_106527,c_89816]) ).

tcf(c_106597,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_106526,c_89611]) ).

tcf(c_106728,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(demodulation,[status(thm)],[c_99045,c_253,c_79573]) ).

tcf(c_106729,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79573,c_106728]) ).

tcf(c_106730,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79414,c_106728]) ).

tcf(c_106731,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_99171,c_106728]) ).

tcf(c_106732,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_106728]) ).

tcf(c_106735,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_252,c_106728]) ).

tcf(c_106737,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_59637,c_106728]) ).

tcf(c_106740,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_255,c_106728]) ).

tcf(c_106741,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m))),
    inference(superposition,[status(thm)],[c_77148,c_106728]) ).

tcf(c_106742,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_106728]) ).

tcf(c_106743,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_12,m)))),
    inference(superposition,[status(thm)],[c_59636,c_106728]) ).

tcf(c_106745,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,sK30(iPr_def_19))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_106728,c_93890]) ).

tcf(c_106746,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_106728,c_1042]) ).

tcf(c_106748,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) ),
    inference(superposition,[status(thm)],[c_106728,c_1024]) ).

tcf(c_106749,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = pls,
    inference(superposition,[status(thm)],[c_106728,c_92002]) ).

tcf(c_106750,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2),
    inference(superposition,[status(thm)],[c_106728,c_252]) ).

tcf(c_106751,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_int_int(times_times_int(X2),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_106728,c_833]) ).

tcf(c_106754,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))),
    inference(superposition,[status(thm)],[c_106728,c_76498]) ).

tcf(c_106758,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_106728,c_217]) ).

tcf(c_106759,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) ),
    inference(superposition,[status(thm)],[c_106728,c_1036]) ).

tcf(c_106760,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),
    inference(superposition,[status(thm)],[c_106728,c_833]) ).

tcf(c_106767,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),pls),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_106728,c_84092]) ).

tcf(c_106768,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),pls))),
    inference(superposition,[status(thm)],[c_106728,c_84084]) ).

tcf(c_106769,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) = pls,
    inference(superposition,[status(thm)],[c_106728,c_83484]) ).

tcf(c_106770,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),sK30(iPr_def_19)) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_106728,c_79573]) ).

tcf(c_106771,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_106728,c_79414]) ).

tcf(c_106781,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_106742,c_103891]) ).

tcf(c_106783,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_106729,c_83504]) ).

tcf(c_106788,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0))),X2)),
    inference(light_normalisation,[status(thm)],[c_106750,c_98072]) ).

tcf(c_106789,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_106731,c_83504]) ).

tcf(c_106890,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_105967]) ).

tcf(c_106891,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_105967]) ).

tcf(c_106892,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_105967]) ).

tcf(c_106893,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_105967]) ).

tcf(c_106895,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_105967]) ).

tcf(c_106896,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_105967]) ).

tcf(c_106898,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_105967]) ).

tcf(c_106899,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_105967]) ).

tcf(c_106900,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_105967]) ).

tcf(c_106901,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_105967]) ).

tcf(c_106902,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_105967]) ).

tcf(c_106903,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_105967]) ).

tcf(c_106904,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_105967]) ).

tcf(c_106905,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_105967]) ).

tcf(c_106906,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_105967]) ).

tcf(c_106907,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_105967]) ).

tcf(c_106908,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_105967]) ).

tcf(c_106909,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_105967]) ).

tcf(c_106910,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_105967]) ).

tcf(c_106911,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_105967]) ).

tcf(c_106912,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_105967]) ).

tcf(c_106913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_105967]) ).

tcf(c_106914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_105967]) ).

tcf(c_106915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_105967]) ).

tcf(c_106916,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_105967]) ).

tcf(c_106917,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_105967]) ).

tcf(c_106918,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_105967]) ).

tcf(c_106919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_105967]) ).

tcf(c_106920,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_105967]) ).

tcf(c_106921,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_105967]) ).

tcf(c_106922,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_105967]) ).

tcf(c_106923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_105967]) ).

tcf(c_106924,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_105967]) ).

tcf(c_106925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_105967]) ).

tcf(c_106926,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_105967]) ).

tcf(c_106927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_105967]) ).

tcf(c_106930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_92656]) ).

tcf(c_106931,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_105967,c_255]) ).

tcf(c_106933,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105967,c_256]) ).

tcf(c_106935,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_105967,c_83532]) ).

tcf(c_106936,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_105967,c_83524]) ).

tcf(c_106937,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_105967]) ).

tcf(c_106939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_95608]) ).

tcf(c_106942,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_105967,c_98014]) ).

tcf(c_106943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_95414]) ).

tcf(c_106944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_95286]) ).

tcf(c_106945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_95041]) ).

tcf(c_106946,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_94695]) ).

tcf(c_106947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_94594]) ).

tcf(c_106948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_93822]) ).

tcf(c_106949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_93551]) ).

tcf(c_106950,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105967,c_79918]) ).

tcf(c_106951,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105967,c_83537]) ).

tcf(c_106952,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105967,c_83534]) ).

tcf(c_106957,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105967,c_96186]) ).

tcf(c_106958,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_106895,c_59636]) ).

tcf(c_106959,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_106890,c_79190]) ).

tcf(c_106960,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_106950,c_76415]) ).

tcf(c_106961,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_106898,c_76855,c_93903]) ).

tcf(c_106965,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_106942,c_79573]) ).

tcf(c_107070,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_102381,c_103848]) ).

tcf(c_107072,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_92656]) ).

tcf(c_107073,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_105916,c_255]) ).

tcf(c_107075,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105916,c_256]) ).

tcf(c_107077,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_105916,c_83532]) ).

tcf(c_107078,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_105916,c_83524]) ).

tcf(c_107079,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_105967]) ).

tcf(c_107081,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_95608]) ).

tcf(c_107084,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_105916,c_98014]) ).

tcf(c_107085,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_95414]) ).

tcf(c_107086,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_95286]) ).

tcf(c_107087,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_95041]) ).

tcf(c_107088,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_94695]) ).

tcf(c_107089,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_94594]) ).

tcf(c_107090,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_93822]) ).

tcf(c_107091,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_93551]) ).

tcf(c_107092,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105916,c_79918]) ).

tcf(c_107093,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105916,c_83537]) ).

tcf(c_107094,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105916,c_83534]) ).

tcf(c_107099,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_105916,c_96186]) ).

tcf(c_107106,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_107084,c_79573]) ).

tcf(c_107110,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_106960]) ).

tcf(c_107111,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_106960]) ).

tcf(c_107112,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_106960]) ).

tcf(c_107113,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_106960]) ).

tcf(c_107115,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_106960]) ).

tcf(c_107116,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_106960]) ).

tcf(c_107118,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_106960]) ).

tcf(c_107119,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_106960]) ).

tcf(c_107120,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_106960]) ).

tcf(c_107121,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_106960]) ).

tcf(c_107122,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_106960]) ).

tcf(c_107123,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_106960]) ).

tcf(c_107124,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_106960]) ).

tcf(c_107125,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_106960]) ).

tcf(c_107126,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_106960]) ).

tcf(c_107127,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_106960]) ).

tcf(c_107128,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_106960]) ).

tcf(c_107129,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_106960]) ).

tcf(c_107130,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_106960]) ).

tcf(c_107131,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_106960]) ).

tcf(c_107132,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_106960]) ).

tcf(c_107133,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_106960]) ).

tcf(c_107134,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_106960]) ).

tcf(c_107135,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_106960]) ).

tcf(c_107136,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_106960]) ).

tcf(c_107137,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_106960]) ).

tcf(c_107138,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_106960]) ).

tcf(c_107139,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_106960]) ).

tcf(c_107140,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_106960]) ).

tcf(c_107141,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_106960]) ).

tcf(c_107142,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_106960]) ).

tcf(c_107143,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_106960]) ).

tcf(c_107144,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_106960]) ).

tcf(c_107145,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_106960]) ).

tcf(c_107146,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_106960]) ).

tcf(c_107147,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_106960]) ).

tcf(c_107148,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_106960]) ).

tcf(c_107149,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_106960]) ).

tcf(c_107152,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_92656]) ).

tcf(c_107153,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_106960,c_255]) ).

tcf(c_107155,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106960,c_256]) ).

tcf(c_107157,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_106960,c_83532]) ).

tcf(c_107158,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_106960,c_83524]) ).

tcf(c_107159,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_106960]) ).

tcf(c_107160,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_105967]) ).

tcf(c_107162,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_95608]) ).

tcf(c_107165,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_106960,c_98014]) ).

tcf(c_107166,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_95414]) ).

tcf(c_107167,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_95286]) ).

tcf(c_107168,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_95041]) ).

tcf(c_107169,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_94695]) ).

tcf(c_107170,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_94594]) ).

tcf(c_107171,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_93822]) ).

tcf(c_107172,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_93551]) ).

tcf(c_107173,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106960,c_79918]) ).

tcf(c_107174,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106960,c_83537]) ).

tcf(c_107175,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106960,c_83534]) ).

tcf(c_107180,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106960,c_96186]) ).

tcf(c_107181,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_107115,c_59636]) ).

tcf(c_107182,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_107110,c_79190]) ).

tcf(c_107183,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_107173,c_76415]) ).

tcf(c_107184,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_107118,c_76855,c_93903]) ).

tcf(c_107188,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_107165,c_79573]) ).

tcf(c_107289,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),
    inference(demodulation,[status(thm)],[c_84333,c_91937]) ).

tcf(c_107291,plain,
    ! [X0: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),one_one_int)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_59636,c_107289]) ).

tcf(c_107292,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_253,c_107289]) ).

tcf(c_107295,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_107289]) ).

tcf(c_107312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),pls))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),pls)),
    inference(superposition,[status(thm)],[c_574,c_107289]) ).

tcf(c_107313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),min))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),min)),
    inference(superposition,[status(thm)],[c_76397,c_107289]) ).

tcf(c_107314,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),one_one_int))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_107289]) ).

tcf(c_107315,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_107289]) ).

tcf(c_107316,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1))),
    inference(superposition,[status(thm)],[c_76399,c_107289]) ).

tcf(c_107317,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2))),
    inference(superposition,[status(thm)],[c_76401,c_107289]) ).

tcf(c_107318,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),m))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),m)),
    inference(superposition,[status(thm)],[c_76402,c_107289]) ).

tcf(c_107319,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s1))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s1)),
    inference(superposition,[status(thm)],[c_76403,c_107289]) ).

tcf(c_107320,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s)),
    inference(superposition,[status(thm)],[c_76404,c_107289]) ).

tcf(c_107321,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),t))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),t)),
    inference(superposition,[status(thm)],[c_76405,c_107289]) ).

tcf(c_107322,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK9))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_107289]) ).

tcf(c_107323,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK10))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_107289]) ).

tcf(c_107324,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK11))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_107289]) ).

tcf(c_107325,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK13))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_107289]) ).

tcf(c_107326,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_14))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_107289]) ).

tcf(c_107327,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_15))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_107289]) ).

tcf(c_107328,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_16))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_107289]) ).

tcf(c_107329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_17))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_107289]) ).

tcf(c_107330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_18))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_107289]) ).

tcf(c_107331,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_107289]) ).

tcf(c_107332,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1))),
    inference(superposition,[status(thm)],[c_77366,c_107289]) ).

tcf(c_107333,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1))),
    inference(superposition,[status(thm)],[c_78024,c_107289]) ).

tcf(c_107334,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,t)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,t))),
    inference(superposition,[status(thm)],[c_78042,c_107289]) ).

tcf(c_107335,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_107289]) ).

tcf(c_107336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_107289]) ).

tcf(c_107338,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79414,c_107289]) ).

tcf(c_107340,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_107289]) ).

tcf(c_107341,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_79918,c_107289]) ).

tcf(c_107343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_80664,c_107289]) ).

tcf(c_107344,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_80677,c_107289]) ).

tcf(c_107345,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m)))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))),
    inference(superposition,[status(thm)],[c_80692,c_107289]) ).

tcf(c_107346,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_107289]) ).

tcf(c_107347,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_107289]) ).

tcf(c_107348,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_107289]) ).

tcf(c_107349,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_107289]) ).

tcf(c_107350,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_96714,c_107289]) ).

tcf(c_107351,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_99171,c_107289]) ).

tcf(c_107352,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_107289]) ).

tcf(c_107353,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_107289]) ).

tcf(c_107355,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_92656]) ).

tcf(c_107356,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X0)),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2),
    inference(superposition,[status(thm)],[c_107289,c_255]) ).

tcf(c_107357,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_107289,c_76880]) ).

tcf(c_107358,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))),
    inference(superposition,[status(thm)],[c_107289,c_256]) ).

tcf(c_107360,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2))),
    inference(superposition,[status(thm)],[c_107289,c_255]) ).

tcf(c_107361,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_106960]) ).

tcf(c_107362,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_105967]) ).

tcf(c_107363,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1))),
    inference(superposition,[status(thm)],[c_107289,c_106496]) ).

tcf(c_107364,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_95608]) ).

tcf(c_107365,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_107289,c_99891]) ).

tcf(c_107367,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X0))),
    inference(superposition,[status(thm)],[c_107289,c_98014]) ).

tcf(c_107368,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_95414]) ).

tcf(c_107369,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_95286]) ).

tcf(c_107370,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_95041]) ).

tcf(c_107371,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_94695]) ).

tcf(c_107372,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_94594]) ).

tcf(c_107373,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_93822]) ).

tcf(c_107374,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_93551]) ).

tcf(c_107375,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_107289,c_79918]) ).

tcf(c_107376,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)))),
    inference(superposition,[status(thm)],[c_107289,c_98897]) ).

tcf(c_107379,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X1))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_107289,c_92625]) ).

tcf(c_107380,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_107289,c_98912]) ).

tcf(c_107381,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),X2)))),
    inference(superposition,[status(thm)],[c_107289,c_98882]) ).

tcf(c_107382,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2))))),
    inference(superposition,[status(thm)],[c_107289,c_98875]) ).

tcf(c_107383,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))))),
    inference(superposition,[status(thm)],[c_107289,c_98873]) ).

tcf(c_107386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_13,iPr_def_14))),X0)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_107318,c_79190]) ).

tcf(c_107528,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X1),X0) = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1693]) ).

tcf(c_107529,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1364]) ).

tcf(c_107530,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),hAPP_nat_nat(minus_minus_nat(number_number_of_nat(X1)),number_number_of_nat(X0))) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_1353,c_594]) ).

tcf(c_107531,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),zero_zero_nat)) = X0,
    inference(superposition,[status(thm)],[c_1353,c_1317]) ).

tcf(c_107532,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X0)) = X0,
    inference(superposition,[status(thm)],[c_1353,c_1358]) ).

tcf(c_107533,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X0),X1))) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1353,c_1320]) ).

tcf(c_107534,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1353,c_1343]) ).

tcf(c_107535,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X0)),X0)) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(superposition,[status(thm)],[c_1353,c_1344]) ).

tcf(c_107536,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X0)) = hAPP_nat_nat(plus_plus_nat(X1),X2) ) ),
    inference(superposition,[status(thm)],[c_1353,c_1352]) ).

tcf(c_107538,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X2),X1)
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X1))) = X2 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1712]) ).

tcf(c_107539,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),one_one_nat)) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_1353,c_77608]) ).

tcf(c_107540,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(iPr_def_10,X0)),X0)) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_1353,c_77614]) ).

tcf(c_107541,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(minus_minus_nat(iPr_def_11),one_one_nat)) = iPr_def_11,
    inference(superposition,[status(thm)],[c_1353,c_78984]) ).

tcf(c_107573,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)) ),
    inference(superposition,[status(thm)],[c_79342,c_1369]) ).

tcf(c_107574,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1286,c_1369]) ).

tcf(c_107575,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1285,c_1369]) ).

tcf(c_107577,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1284,c_1369]) ).

tcf(c_107578,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),hAPP_nat_nat(iPr_def_10,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_77521,c_1369]) ).

tcf(c_107579,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1)) ),
    inference(superposition,[status(thm)],[c_94015,c_1369]) ).

tcf(c_107582,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(iPr_def_10,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_59634,c_1369]) ).

tcf(c_107583,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1369,c_1590]) ).

tcf(c_107584,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X0),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1369,c_1026]) ).

tcf(c_107585,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(times_times_nat(X0),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1369,c_1023]) ).

tcf(c_107618,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X0)))) ),
    inference(superposition,[status(thm)],[c_1286,c_1370]) ).

tcf(c_107619,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)))) ),
    inference(superposition,[status(thm)],[c_1285,c_1370]) ).

tcf(c_107621,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1284,c_1370]) ).

tcf(c_107623,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1))) ),
    inference(superposition,[status(thm)],[c_94015,c_1370]) ).

tcf(c_107626,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),hAPP_nat_nat(iPr_def_10,X0))) ),
    inference(superposition,[status(thm)],[c_59634,c_1370]) ).

tcf(c_107650,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),sK18(number_number_of_nat(X0),number_number_of_nat(X1))) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_131,c_1376]) ).

tcf(c_107652,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK18(zero_zero_nat,X0)) = X0,
    inference(superposition,[status(thm)],[c_1330,c_1376]) ).

tcf(c_107653,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(one_one_nat),sK18(one_one_nat,hAPP_nat_nat(power_power_nat(X0),X1))) = hAPP_nat_nat(power_power_nat(X0),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_699,c_1376]) ).

tcf(c_107654,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,X0)) = X0,
    inference(superposition,[status(thm)],[c_1365,c_1376]) ).

tcf(c_107655,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,X1)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1295,c_1376]) ).

tcf(c_107656,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),sK18(hAPP_nat_nat(minus_minus_nat(X0),X1),X0)) = X0,
    inference(superposition,[status(thm)],[c_1299,c_1376]) ).

tcf(c_107657,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(plus_plus_nat(X1),X0))) = hAPP_nat_nat(plus_plus_nat(X1),X0),
    inference(superposition,[status(thm)],[c_1373,c_1376]) ).

tcf(c_107658,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(plus_plus_nat(X0),X1))) = hAPP_nat_nat(plus_plus_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1375,c_1376]) ).

tcf(c_107659,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)))) = hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)),
    inference(superposition,[status(thm)],[c_1408,c_1376]) ).

tcf(c_107660,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(times_times_nat(X0),X0))) = hAPP_nat_nat(times_times_nat(X0),X0),
    inference(superposition,[status(thm)],[c_1409,c_1376]) ).

tcf(c_107661,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,sK35(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))) = sK35(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1376]) ).

tcf(c_107662,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(div_mod_nat(X0),X1)),sK18(hAPP_nat_nat(div_mod_nat(X0),X1),X0)) = X0,
    inference(superposition,[status(thm)],[c_1694,c_1376]) ).

tcf(c_107663,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X1),sK18(X1,hAPP_nat_nat(div_mod_nat(X0),X2))) = hAPP_nat_nat(div_mod_nat(X0),X2) )
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1376]) ).

tcf(c_107664,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(iPr_def_10,X0))) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_76584,c_1376]) ).

tcf(c_107665,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(one_one_nat),sK18(one_one_nat,hAPP_nat_nat(iPr_def_10,X0))) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_76588,c_1376]) ).

tcf(c_107666,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),sK18(one_one_nat,iPr_def_11)) = iPr_def_11,
    inference(superposition,[status(thm)],[c_76648,c_1376]) ).

tcf(c_107667,plain,
    hAPP_nat_nat(iPr_def_10,sK18(one_one_nat,iPr_def_11)) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_107666,c_59634]) ).

tcf(c_107668,plain,
    ! [X0: $i] : hAPP_nat_nat(iPr_def_10,sK18(one_one_nat,hAPP_nat_nat(iPr_def_10,X0))) = hAPP_nat_nat(iPr_def_10,X0),
    inference(light_normalisation,[status(thm)],[c_107665,c_59634]) ).

tcf(c_107675,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(iPr_def_10,sK18(one_one_nat,hAPP_nat_nat(power_power_nat(X0),X1))) = hAPP_nat_nat(power_power_nat(X0),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(light_normalisation,[status(thm)],[c_107653,c_59634]) ).

tcf(c_107728,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK18(one_one_nat,iPr_def_11)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_107667,c_102906]) ).

tcf(c_107729,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),sK18(one_one_nat,iPr_def_11))),
    inference(superposition,[status(thm)],[c_107667,c_77614]) ).

tcf(c_107732,plain,
    hAPP_nat_nat(minus_minus_nat(iPr_def_11),one_one_nat) = sK18(one_one_nat,iPr_def_11),
    inference(superposition,[status(thm)],[c_107667,c_77549]) ).

tcf(c_107733,plain,
    hAPP_nat_nat(minus_minus_nat(iPr_def_11),sK18(one_one_nat,iPr_def_11)) = one_one_nat,
    inference(superposition,[status(thm)],[c_107667,c_77538]) ).

tcf(c_107734,plain,
    sK18(one_one_nat,iPr_def_11) != iPr_def_11,
    inference(superposition,[status(thm)],[c_107667,c_78756]) ).

tcf(c_107739,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK18(one_one_nat,iPr_def_11)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_107667,c_76584]) ).

tcf(c_107740,plain,
    sK18(one_one_nat,iPr_def_11) = one_one_nat,
    inference(light_normalisation,[status(thm)],[c_107732,c_78900]) ).

tcf(c_107741,plain,
    hAPP_nat_nat(iPr_def_10,one_one_nat) = iPr_def_11,
    inference(demodulation,[status(thm)],[c_107667,c_107740]) ).

tcf(c_107772,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_79557,c_98913]) ).

tcf(c_107773,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_98913]) ).

tcf(c_107774,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_99171,c_98913]) ).

tcf(c_107775,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_98913]) ).

tcf(c_107776,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98913]) ).

tcf(c_107781,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_98913]) ).

tcf(c_107782,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76855,c_98913]) ).

tcf(c_107789,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1))),
    inference(superposition,[status(thm)],[c_93890,c_98913]) ).

tcf(c_107790,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1))),
    inference(superposition,[status(thm)],[c_78930,c_98913]) ).

tcf(c_107791,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))),
    inference(superposition,[status(thm)],[c_78938,c_98913]) ).

tcf(c_107792,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))),
    inference(superposition,[status(thm)],[c_79190,c_98913]) ).

tcf(c_107793,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1))),
    inference(superposition,[status(thm)],[c_79161,c_98913]) ).

tcf(c_107794,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1))),
    inference(superposition,[status(thm)],[c_79901,c_98913]) ).

tcf(c_107795,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79904,c_98913]) ).

tcf(c_107796,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0))),
    inference(superposition,[status(thm)],[c_83594,c_98913]) ).

tcf(c_107798,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_85658,c_98913]) ).

tcf(c_107799,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88494,c_98913]) ).

tcf(c_107800,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88513,c_98913]) ).

tcf(c_107801,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88550,c_98913]) ).

tcf(c_107805,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93551,c_98913]) ).

tcf(c_107822,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1))),
    inference(superposition,[status(thm)],[c_107289,c_98913]) ).

tcf(c_107824,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),pls),X2)) ),
    inference(superposition,[status(thm)],[c_98913,c_897]) ).

tcf(c_107825,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) ),
    inference(superposition,[status(thm)],[c_98913,c_896]) ).

tcf(c_107826,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls),
    inference(light_normalisation,[status(thm)],[c_107781,c_574]) ).

tcf(c_107827,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_107796,c_59637,c_77366]) ).

tcf(c_107829,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_107792,c_99243]) ).

tcf(c_107830,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_107782,c_102421]) ).

tcf(c_107833,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107789,c_93903,c_99172]) ).

tcf(c_107838,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_107775,c_79918]) ).

tcf(c_107839,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_107799,c_88957]) ).

tcf(c_107840,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107801,c_89816]) ).

tcf(c_107841,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107800,c_89611]) ).

tcf(c_107881,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_79557,c_98914]) ).

tcf(c_107882,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_98914]) ).

tcf(c_107883,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_99171,c_98914]) ).

tcf(c_107884,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_98914]) ).

tcf(c_107885,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98914]) ).

tcf(c_107890,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_98914]) ).

tcf(c_107891,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76855,c_98914]) ).

tcf(c_107898,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1))),
    inference(superposition,[status(thm)],[c_93890,c_98914]) ).

tcf(c_107899,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1))),
    inference(superposition,[status(thm)],[c_78930,c_98914]) ).

tcf(c_107900,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))),
    inference(superposition,[status(thm)],[c_78938,c_98914]) ).

tcf(c_107901,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))),
    inference(superposition,[status(thm)],[c_79190,c_98914]) ).

tcf(c_107902,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1))),
    inference(superposition,[status(thm)],[c_79161,c_98914]) ).

tcf(c_107903,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1))),
    inference(superposition,[status(thm)],[c_79901,c_98914]) ).

tcf(c_107904,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79904,c_98914]) ).

tcf(c_107905,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0))),
    inference(superposition,[status(thm)],[c_83594,c_98914]) ).

tcf(c_107907,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_85658,c_98914]) ).

tcf(c_107908,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88494,c_98914]) ).

tcf(c_107909,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88513,c_98914]) ).

tcf(c_107910,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88550,c_98914]) ).

tcf(c_107914,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93551,c_98914]) ).

tcf(c_107931,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1))),
    inference(superposition,[status(thm)],[c_107289,c_98914]) ).

tcf(c_107936,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_nat_nat(times_times_nat(one_one_nat),X2)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2),
    inference(superposition,[status(thm)],[c_98914,c_676]) ).

tcf(c_107938,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_98914,c_805]) ).

tcf(c_107939,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls),
    inference(light_normalisation,[status(thm)],[c_107890,c_574]) ).

tcf(c_107940,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_107905,c_59637,c_77366]) ).

tcf(c_107942,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_107901,c_99243]) ).

tcf(c_107943,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_107891,c_102421]) ).

tcf(c_107946,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107898,c_93903,c_99172]) ).

tcf(c_107947,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_107884,c_79918]) ).

tcf(c_107948,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_107908,c_88957]) ).

tcf(c_107949,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107910,c_89816]) ).

tcf(c_107950,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_107909,c_89611]) ).

tcf(c_107996,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_79557,c_98916]) ).

tcf(c_107997,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_98916]) ).

tcf(c_107998,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_99171,c_98916]) ).

tcf(c_107999,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_98916]) ).

tcf(c_108000,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X0)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98916]) ).

tcf(c_108005,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_98916]) ).

tcf(c_108006,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(m),X0)))),
    inference(superposition,[status(thm)],[c_76855,c_98916]) ).

tcf(c_108013,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)),X1))),
    inference(superposition,[status(thm)],[c_93890,c_98916]) ).

tcf(c_108014,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))),X1))),
    inference(superposition,[status(thm)],[c_78930,c_98916]) ).

tcf(c_108015,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X0))),
    inference(superposition,[status(thm)],[c_78938,c_98916]) ).

tcf(c_108016,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))),
    inference(superposition,[status(thm)],[c_79190,c_98916]) ).

tcf(c_108017,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))),X1))),
    inference(superposition,[status(thm)],[c_79161,c_98916]) ).

tcf(c_108018,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))),X1))),
    inference(superposition,[status(thm)],[c_79901,c_98916]) ).

tcf(c_108019,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X0))),
    inference(superposition,[status(thm)],[c_79904,c_98916]) ).

tcf(c_108020,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X0))),
    inference(superposition,[status(thm)],[c_83594,c_98916]) ).

tcf(c_108022,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_85658,c_98916]) ).

tcf(c_108023,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X0))),
    inference(superposition,[status(thm)],[c_88494,c_98916]) ).

tcf(c_108024,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88513,c_98916]) ).

tcf(c_108025,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88550,c_98916]) ).

tcf(c_108029,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_93551,c_98916]) ).

tcf(c_108046,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1))),
    inference(superposition,[status(thm)],[c_107289,c_98916]) ).

tcf(c_108048,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98916,c_92656]) ).

tcf(c_108049,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2),
    inference(superposition,[status(thm)],[c_98916,c_255]) ).

tcf(c_108051,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),
    inference(superposition,[status(thm)],[c_98916,c_256]) ).

tcf(c_108053,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls),
    inference(light_normalisation,[status(thm)],[c_108005,c_574]) ).

tcf(c_108054,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)),
    inference(light_normalisation,[status(thm)],[c_108020,c_59637,c_77366]) ).

tcf(c_108056,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_108016,c_99243]) ).

tcf(c_108057,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_108006,c_102421]) ).

tcf(c_108060,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_108013,c_93903,c_99172]) ).

tcf(c_108061,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(light_normalisation,[status(thm)],[c_107999,c_79918]) ).

tcf(c_108062,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X0))),
    inference(light_normalisation,[status(thm)],[c_108023,c_88957]) ).

tcf(c_108063,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_108025,c_89816]) ).

tcf(c_108064,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(light_normalisation,[status(thm)],[c_108024,c_89611]) ).

tcf(c_108132,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79573,c_99039]) ).

tcf(c_108133,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79414,c_99039]) ).

tcf(c_108134,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_99171,c_99039]) ).

tcf(c_108135,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_99039]) ).

tcf(c_108140,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_59637,c_99039]) ).

tcf(c_108144,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m))),
    inference(superposition,[status(thm)],[c_77148,c_99039]) ).

tcf(c_108145,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_99039]) ).

tcf(c_108148,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),pls),X2)) ),
    inference(superposition,[status(thm)],[c_99039,c_897]) ).

tcf(c_108149,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) ),
    inference(superposition,[status(thm)],[c_99039,c_896]) ).

tcf(c_108151,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_108145,c_103891]) ).

tcf(c_108158,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_108134,c_83504]) ).

tcf(c_108186,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79573,c_99040]) ).

tcf(c_108187,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79414,c_99040]) ).

tcf(c_108188,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_99171,c_99040]) ).

tcf(c_108189,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_99040]) ).

tcf(c_108194,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_59637,c_99040]) ).

tcf(c_108198,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m))),
    inference(superposition,[status(thm)],[c_77148,c_99040]) ).

tcf(c_108199,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_99040]) ).

tcf(c_108205,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_nat_nat(times_times_nat(one_one_nat),X2)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2),
    inference(superposition,[status(thm)],[c_99040,c_676]) ).

tcf(c_108207,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_99040,c_805]) ).

tcf(c_108209,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_108199,c_103891]) ).

tcf(c_108212,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_108188,c_83504]) ).

tcf(c_108222,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),X0) = pls,
    inference(demodulation,[status(thm)],[c_84334,c_91937]) ).

tcf(c_108223,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_108222]) ).

tcf(c_108224,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)),X1) = pls,
    inference(superposition,[status(thm)],[c_253,c_108222]) ).

tcf(c_108226,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X2)))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_108222]) ).

tcf(c_108227,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_108222]) ).

tcf(c_108230,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_108222]) ).

tcf(c_108231,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_253,c_108222]) ).

tcf(c_108234,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)))),X0) = pls,
    inference(superposition,[status(thm)],[c_93551,c_108222]) ).

tcf(c_108251,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),pls)))),X0) = pls,
    inference(superposition,[status(thm)],[c_574,c_108222]) ).

tcf(c_108252,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),min)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76397,c_108222]) ).

tcf(c_108253,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),one_one_int)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76393,c_108222]) ).

tcf(c_108254,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),undefined_int(int))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76395,c_108222]) ).

tcf(c_108255,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76399,c_108222]) ).

tcf(c_108256,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X1,X2))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76401,c_108222]) ).

tcf(c_108257,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),m)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76402,c_108222]) ).

tcf(c_108258,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s1)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76403,c_108222]) ).

tcf(c_108259,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76404,c_108222]) ).

tcf(c_108260,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),t)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76405,c_108222]) ).

tcf(c_108261,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK9)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76406,c_108222]) ).

tcf(c_108262,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK10)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76407,c_108222]) ).

tcf(c_108263,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76408,c_108222]) ).

tcf(c_108264,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK13)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76409,c_108222]) ).

tcf(c_108265,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_14)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76410,c_108222]) ).

tcf(c_108266,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_15)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76411,c_108222]) ).

tcf(c_108267,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_16)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76412,c_108222]) ).

tcf(c_108268,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_17)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76413,c_108222]) ).

tcf(c_108269,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_18)))),X0) = pls,
    inference(superposition,[status(thm)],[c_76414,c_108222]) ).

tcf(c_108270,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X0) = pls,
    inference(superposition,[status(thm)],[c_76415,c_108222]) ).

tcf(c_108271,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_77366,c_108222]) ).

tcf(c_108272,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78024,c_108222]) ).

tcf(c_108273,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,t))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78042,c_108222]) ).

tcf(c_108274,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X1,one_one_int))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78056,c_108222]) ).

tcf(c_108275,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))))),X0) = pls,
    inference(superposition,[status(thm)],[c_78203,c_108222]) ).

tcf(c_108277,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79414,c_108222]) ).

tcf(c_108279,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79437,c_108222]) ).

tcf(c_108280,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_79918,c_108222]) ).

tcf(c_108282,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80664,c_108222]) ).

tcf(c_108283,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80677,c_108222]) ).

tcf(c_108284,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),m))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80692,c_108222]) ).

tcf(c_108285,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_80705,c_108222]) ).

tcf(c_108286,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88502,c_108222]) ).

tcf(c_108287,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88521,c_108222]) ).

tcf(c_108288,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_88558,c_108222]) ).

tcf(c_108289,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_96714,c_108222]) ).

tcf(c_108290,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99171,c_108222]) ).

tcf(c_108291,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))))),X0) = pls,
    inference(superposition,[status(thm)],[c_100498,c_108222]) ).

tcf(c_108292,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))))),X0) = pls,
    inference(superposition,[status(thm)],[c_103848,c_108222]) ).

tcf(c_108293,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),pls))),
    inference(superposition,[status(thm)],[c_108222,c_76662]) ).

tcf(c_108295,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),pls),X0)),
    inference(superposition,[status(thm)],[c_108222,c_1698]) ).

tcf(c_108297,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_13,iPr_def_14)))),X0) = pls,
    inference(light_normalisation,[status(thm)],[c_108257,c_79190]) ).

tcf(c_108470,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_79342,c_1379]) ).

tcf(c_108471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1286,c_1379]) ).

tcf(c_108472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1285,c_1379]) ).

tcf(c_108475,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(iPr_def_10,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_77521,c_1379]) ).

tcf(c_108476,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X2)),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_94015,c_1379]) ).

tcf(c_108477,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1326,c_1379]) ).

tcf(c_108479,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(iPr_def_10,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_59634,c_1379]) ).

tcf(c_108480,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(plus_plus_nat(X1),X2))) = hAPP_nat_nat(plus_plus_nat(X1),X2) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1379,c_1376]) ).

tcf(c_108481,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1379,c_1332]) ).

tcf(c_108509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X3),X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1286,c_1380]) ).

tcf(c_108510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X3),X2))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1285,c_1380]) ).

tcf(c_108514,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X1)),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_94015,c_1380]) ).

tcf(c_108518,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK18(X0,hAPP_nat_nat(plus_plus_nat(X2),X1))) = hAPP_nat_nat(plus_plus_nat(X2),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1380,c_1376]) ).

tcf(c_108519,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1380,c_1332]) ).

tcf(c_108629,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1295,c_1385]) ).

tcf(c_108631,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X0)),X2))),
    inference(superposition,[status(thm)],[c_1375,c_1385]) ).

tcf(c_108632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1379,c_1385]) ).

tcf(c_108633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X3),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1380,c_1385]) ).

tcf(c_108634,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X1),X0))))),
    inference(superposition,[status(thm)],[c_1408,c_1385]) ).

tcf(c_108635,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X1),X0)),hAPP_nat_nat(plus_plus_nat(X1),X0)))),
    inference(superposition,[status(thm)],[c_1409,c_1385]) ).

tcf(c_108636,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sK35(X2,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1577,c_1385]) ).

tcf(c_108637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(div_mod_nat(X0),X3)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) ),
    inference(superposition,[status(thm)],[c_1711,c_1385]) ).

tcf(c_108638,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X1),X0)))),
    inference(superposition,[status(thm)],[c_76584,c_1385]) ).

tcf(c_108640,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(iPr_def_11),X0)),X1)) ),
    inference(superposition,[status(thm)],[c_79342,c_1385]) ).

tcf(c_108641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1286,c_1385]) ).

tcf(c_108642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1285,c_1385]) ).

tcf(c_108645,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(iPr_def_10,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_77521,c_1385]) ).

tcf(c_108646,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_94015,c_1385]) ).

tcf(c_108648,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1325,c_1385]) ).

tcf(c_108649,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(iPr_def_10,X0)),X1)) ),
    inference(superposition,[status(thm)],[c_59634,c_1385]) ).

tcf(c_108688,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1295,c_1386]) ).

tcf(c_108690,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X2))),
    inference(superposition,[status(thm)],[c_1375,c_1386]) ).

tcf(c_108691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X2),X3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1379,c_1386]) ).

tcf(c_108692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X3),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1380,c_1386]) ).

tcf(c_108693,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X1))))),
    inference(superposition,[status(thm)],[c_1408,c_1386]) ).

tcf(c_108694,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(X0),X1)))),
    inference(superposition,[status(thm)],[c_1409,c_1386]) ).

tcf(c_108695,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),zero_zero_nat))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK35(X2,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_1577,c_1386]) ).

tcf(c_108696,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(div_mod_nat(X0),X3)))
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) ),
    inference(superposition,[status(thm)],[c_1711,c_1386]) ).

tcf(c_108697,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(plus_plus_nat(X0),X1)))),
    inference(superposition,[status(thm)],[c_76584,c_1386]) ).

tcf(c_108700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1286,c_1386]) ).

tcf(c_108701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),X3)) ),
    inference(superposition,[status(thm)],[c_1285,c_1386]) ).

tcf(c_108705,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1)),X2)) ),
    inference(superposition,[status(thm)],[c_94015,c_1386]) ).

tcf(c_108794,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(demodulation,[status(thm)],[c_108270,c_253]) ).

tcf(c_108795,plain,
    hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),iPr_def_11)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = pls,
    inference(superposition,[status(thm)],[c_82861,c_108794]) ).

tcf(c_108796,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),X0) = pls,
    inference(superposition,[status(thm)],[c_253,c_108794]) ).

tcf(c_108798,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),hAPP_int_int(times_times_int(X0),X1)) = pls,
    inference(superposition,[status(thm)],[c_252,c_108794]) ).

tcf(c_108799,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(times_times_int(X0),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X0) = pls,
    inference(superposition,[status(thm)],[c_217,c_108794]) ).

tcf(c_108802,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),m) = pls,
    inference(superposition,[status(thm)],[c_59637,c_108794]) ).

tcf(c_108803,plain,
    ! [X0: $i] : hBOOL(member_int(X0,zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls))),
    inference(superposition,[status(thm)],[c_108794,c_76662]) ).

tcf(c_108805,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls),X0)),
    inference(superposition,[status(thm)],[c_108794,c_1698]) ).

tcf(c_108814,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79573,c_99042]) ).

tcf(c_108815,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_79414,c_99042]) ).

tcf(c_108816,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_99171,c_99042]) ).

tcf(c_108817,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X0),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_99042]) ).

tcf(c_108822,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),m)))),
    inference(superposition,[status(thm)],[c_59637,c_99042]) ).

tcf(c_108826,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),m))),
    inference(superposition,[status(thm)],[c_77148,c_99042]) ).

tcf(c_108827,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_99042]) ).

tcf(c_108830,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99042,c_92656]) ).

tcf(c_108831,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2),
    inference(superposition,[status(thm)],[c_99042,c_255]) ).

tcf(c_108833,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),
    inference(superposition,[status(thm)],[c_99042,c_256]) ).

tcf(c_108836,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(iPr_def_13,iPr_def_14))),
    inference(light_normalisation,[status(thm)],[c_108827,c_103891]) ).

tcf(c_108839,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_108816,c_83504]) ).

tcf(c_108857,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_92656]) ).

tcf(c_108858,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_106906,c_255]) ).

tcf(c_108860,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106906,c_256]) ).

tcf(c_108862,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_106906,c_83532]) ).

tcf(c_108863,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_106906,c_83524]) ).

tcf(c_108867,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_106960]) ).

tcf(c_108868,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_105967]) ).

tcf(c_108870,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_95608]) ).

tcf(c_108873,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_106906,c_98014]) ).

tcf(c_108874,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_95414]) ).

tcf(c_108875,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_95286]) ).

tcf(c_108876,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_95041]) ).

tcf(c_108877,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_94695]) ).

tcf(c_108878,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_94594]) ).

tcf(c_108879,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_93822]) ).

tcf(c_108880,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_93551]) ).

tcf(c_108881,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106906,c_79918]) ).

tcf(c_108884,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106906,c_83537]) ).

tcf(c_108885,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106906,c_83534]) ).

tcf(c_108890,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_106906,c_96186]) ).

tcf(c_108897,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_108873,c_79573]) ).

tcf(c_108910,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_107183]) ).

tcf(c_108911,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_107183]) ).

tcf(c_108912,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_107183]) ).

tcf(c_108913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_107183]) ).

tcf(c_108915,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_107183]) ).

tcf(c_108916,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_107183]) ).

tcf(c_108918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_107183]) ).

tcf(c_108919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_107183]) ).

tcf(c_108920,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_107183]) ).

tcf(c_108921,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_107183]) ).

tcf(c_108922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_107183]) ).

tcf(c_108923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_107183]) ).

tcf(c_108924,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_107183]) ).

tcf(c_108925,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_107183]) ).

tcf(c_108926,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_107183]) ).

tcf(c_108927,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_107183]) ).

tcf(c_108928,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_107183]) ).

tcf(c_108929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_107183]) ).

tcf(c_108930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_107183]) ).

tcf(c_108931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_107183]) ).

tcf(c_108932,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_107183]) ).

tcf(c_108933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_107183]) ).

tcf(c_108934,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_107183]) ).

tcf(c_108935,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_107183]) ).

tcf(c_108936,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_107183]) ).

tcf(c_108937,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_107183]) ).

tcf(c_108938,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_107183]) ).

tcf(c_108939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_107183]) ).

tcf(c_108940,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_107183]) ).

tcf(c_108941,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_107183]) ).

tcf(c_108942,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_107183]) ).

tcf(c_108943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_107183]) ).

tcf(c_108944,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_107183]) ).

tcf(c_108945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_107183]) ).

tcf(c_108946,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_107183]) ).

tcf(c_108947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_107183]) ).

tcf(c_108948,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_107183]) ).

tcf(c_108949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_107183]) ).

tcf(c_108950,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_107183]) ).

tcf(c_108951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_107183]) ).

tcf(c_108953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_107183]) ).

tcf(c_108955,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_92656]) ).

tcf(c_108956,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_107183,c_255]) ).

tcf(c_108958,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107183,c_256]) ).

tcf(c_108960,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_107183,c_83532]) ).

tcf(c_108961,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_107183,c_83524]) ).

tcf(c_108962,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_107183]) ).

tcf(c_108966,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_106960]) ).

tcf(c_108967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_105967]) ).

tcf(c_108969,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_95608]) ).

tcf(c_108972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_107183,c_98014]) ).

tcf(c_108973,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_95414]) ).

tcf(c_108974,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_95286]) ).

tcf(c_108975,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_95041]) ).

tcf(c_108976,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_94695]) ).

tcf(c_108977,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_94594]) ).

tcf(c_108978,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_93822]) ).

tcf(c_108979,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_93551]) ).

tcf(c_108980,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107183,c_79918]) ).

tcf(c_108983,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107183,c_83537]) ).

tcf(c_108984,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107183,c_83534]) ).

tcf(c_108989,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107183,c_96186]) ).

tcf(c_108990,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_108915,c_59636]) ).

tcf(c_108991,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_108910,c_79190]) ).

tcf(c_108992,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_108980,c_76415]) ).

tcf(c_108993,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_108918,c_76855,c_93903]) ).

tcf(c_108997,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_108972,c_79573]) ).

tcf(c_109219,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_92656]) ).

tcf(c_109220,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_107126,c_255]) ).

tcf(c_109222,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107126,c_256]) ).

tcf(c_109224,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_107126,c_83532]) ).

tcf(c_109225,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_107126,c_83524]) ).

tcf(c_109226,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_107183]) ).

tcf(c_109230,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_106960]) ).

tcf(c_109231,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_105967]) ).

tcf(c_109233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_95608]) ).

tcf(c_109236,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_107126,c_98014]) ).

tcf(c_109237,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_95414]) ).

tcf(c_109238,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_95286]) ).

tcf(c_109239,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_95041]) ).

tcf(c_109240,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_94695]) ).

tcf(c_109241,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_94594]) ).

tcf(c_109242,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_93822]) ).

tcf(c_109243,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_93551]) ).

tcf(c_109244,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107126,c_79918]) ).

tcf(c_109247,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107126,c_83537]) ).

tcf(c_109248,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107126,c_83534]) ).

tcf(c_109253,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_107126,c_96186]) ).

tcf(c_109260,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_109236,c_79573]) ).

tcf(c_109268,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1443]) ).

tcf(c_109270,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1353,c_1443]) ).

tcf(c_109271,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1259,c_1443]) ).

tcf(c_109272,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X0),iPr_def_11))) ),
    inference(superposition,[status(thm)],[c_82316,c_1443]) ).

tcf(c_109274,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_1308,c_1443]) ).

tcf(c_109275,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_218,c_1443]) ).

tcf(c_109281,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1337,c_1443]) ).

tcf(c_109302,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1444]) ).

tcf(c_109304,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X1))) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1353,c_1444]) ).

tcf(c_109305,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat))
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1259,c_1444]) ).

tcf(c_109308,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_1308,c_1444]) ).

tcf(c_109309,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)))) ),
    inference(superposition,[status(thm)],[c_218,c_1444]) ).

tcf(c_109331,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( X0 = one_one_nat )
      | ( hAPP_nat_nat(power_power_nat(X0),iPr_def_11) != X0 ) ),
    inference(superposition,[status(thm)],[c_82316,c_1445]) ).

tcf(c_109333,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != hAPP_nat_nat(times_times_nat(X0),X1) ) ),
    inference(superposition,[status(thm)],[c_1308,c_1445]) ).

tcf(c_109334,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = zero_zero_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X2) = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)) != X1 ) ),
    inference(superposition,[status(thm)],[c_218,c_1445]) ).

tcf(c_109336,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = zero_zero_nat )
      | ( X0 = one_one_nat )
      | ( hAPP_nat_nat(times_times_nat(X0),X1) != X1 ) ),
    inference(superposition,[status(thm)],[c_1309,c_1445]) ).

tcf(c_109360,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X0),one_one_int)),X0)),
    inference(superposition,[status(thm)],[c_114,c_1517]) ).

tcf(c_109361,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(hAPP_i1948725293t_bool(ord_less_eq_int,X0)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1563,c_1517]) ).

tcf(c_109362,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
      | sP3(X0,hAPP_int_int(minus_minus_int(X1),one_one_int),X2) ),
    inference(superposition,[status(thm)],[c_46418,c_1517]) ).

tcf(c_109364,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(iPr_def_12,X0)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(minus_minus_int(X1),one_one_int))) ),
    inference(superposition,[status(thm)],[c_90614,c_1517]) ).

tcf(c_109365,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(minus_minus_int(X0),one_one_int)),X1)) ),
    inference(superposition,[status(thm)],[c_1720,c_1517]) ).

tcf(c_109366,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_78632,c_1517]) ).

tcf(c_109371,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,X1))
      | sP3(X0,hAPP_int_int(minus_minus_int(X1),one_one_int),X2) ),
    inference(light_normalisation,[status(thm)],[c_109362,c_59643]) ).

tcf(c_109384,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_nat_int(power_power_int(X0),iPr_def_11)),X0)),
    inference(superposition,[status(thm)],[c_82861,c_78295]) ).

tcf(c_109385,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),X1)),X0)),
    inference(superposition,[status(thm)],[c_253,c_78295]) ).

tcf(c_109387,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),X2)),
    inference(superposition,[status(thm)],[c_252,c_78295]) ).

tcf(c_109388,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))),hAPP_int_int(times_times_int(X0),X2))),
    inference(superposition,[status(thm)],[c_217,c_78295]) ).

tcf(c_109391,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,number_number_of_int(hAPP_int_int(times_times_int(X0),X1))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_382,c_78295]) ).

tcf(c_109393,plain,
    hBOOL(hAPP_int_bool(zcong(pls,one_one_int),min)),
    inference(superposition,[status(thm)],[c_79464,c_78295]) ).

tcf(c_109395,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_15),one_one_int)),
    inference(superposition,[status(thm)],[c_76925,c_78295]) ).

tcf(c_109396,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_16),one_one_int)),
    inference(superposition,[status(thm)],[c_76926,c_78295]) ).

tcf(c_109397,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_17),one_one_int)),
    inference(superposition,[status(thm)],[c_76927,c_78295]) ).

tcf(c_109398,plain,
    hBOOL(hAPP_int_bool(zcong(pls,iPr_def_18),one_one_int)),
    inference(superposition,[status(thm)],[c_76928,c_78295]) ).

tcf(c_109400,plain,
    hBOOL(hAPP_int_bool(zcong(pls,undefined_int(int)),undefined_int(int))),
    inference(superposition,[status(thm)],[c_77063,c_78295]) ).

tcf(c_109401,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,twoSqu1241645765sum2sq(X0)),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_77069,c_78295]) ).

tcf(c_109402,plain,
    hBOOL(hAPP_int_bool(zcong(pls,sK26(iPr_def_14)),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78201,c_78295]) ).

tcf(c_109403,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(plus_plus_int(X0),X0)),X0)),
    inference(superposition,[status(thm)],[c_79150,c_78295]) ).

tcf(c_109405,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),X1)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_83537,c_78295]) ).

tcf(c_109406,plain,
    hBOOL(hAPP_int_bool(zcong(pls,sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88500,c_78295]) ).

tcf(c_109407,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88519,c_78295]) ).

tcf(c_109408,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88556,c_78295]) ).

tcf(c_109409,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_96186,c_78295]) ).

tcf(c_109410,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))),
    inference(superposition,[status(thm)],[c_98014,c_78295]) ).

tcf(c_109411,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))),
    inference(superposition,[status(thm)],[c_98014,c_78295]) ).

tcf(c_109412,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))),
    inference(superposition,[status(thm)],[c_106496,c_78295]) ).

tcf(c_109413,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))),
    inference(superposition,[status(thm)],[c_106728,c_78295]) ).

tcf(c_109415,plain,
    ! [X0: $i,X1: $i] : hBOOL(member_int(X0,zcong(pls,hAPP_int_int(times_times_int(X1),X0)))),
    inference(superposition,[status(thm)],[c_78295,c_226]) ).

tcf(c_109416,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK14(pls,hAPP_int_int(times_times_int(X0),X1),X1))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_78295,c_852]) ).

tcf(c_109482,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_108992]) ).

tcf(c_109483,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_108992]) ).

tcf(c_109484,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_108992]) ).

tcf(c_109485,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_108992]) ).

tcf(c_109487,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_108992]) ).

tcf(c_109488,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_108992]) ).

tcf(c_109490,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_108992]) ).

tcf(c_109491,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_108992]) ).

tcf(c_109492,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_108992]) ).

tcf(c_109493,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_108992]) ).

tcf(c_109494,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_108992]) ).

tcf(c_109495,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_108992]) ).

tcf(c_109496,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_108992]) ).

tcf(c_109497,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_108992]) ).

tcf(c_109498,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_108992]) ).

tcf(c_109499,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_108992]) ).

tcf(c_109500,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_108992]) ).

tcf(c_109501,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_108992]) ).

tcf(c_109502,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_108992]) ).

tcf(c_109503,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_108992]) ).

tcf(c_109504,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_108992]) ).

tcf(c_109505,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_108992]) ).

tcf(c_109506,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_108992]) ).

tcf(c_109507,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_108992]) ).

tcf(c_109508,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_108992]) ).

tcf(c_109509,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_108992]) ).

tcf(c_109510,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_108992]) ).

tcf(c_109511,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_108992]) ).

tcf(c_109512,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_108992]) ).

tcf(c_109513,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_108992]) ).

tcf(c_109514,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_108992]) ).

tcf(c_109515,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_108992]) ).

tcf(c_109516,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_108992]) ).

tcf(c_109517,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_108992]) ).

tcf(c_109518,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_108992]) ).

tcf(c_109519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_108992]) ).

tcf(c_109520,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_108992]) ).

tcf(c_109521,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_108992]) ).

tcf(c_109522,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_108992]) ).

tcf(c_109523,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_108992]) ).

tcf(c_109524,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_108992]) ).

tcf(c_109525,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_108992]) ).

tcf(c_109526,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_108992]) ).

tcf(c_109529,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_92656]) ).

tcf(c_109530,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_108992,c_255]) ).

tcf(c_109532,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108992,c_256]) ).

tcf(c_109534,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_108992,c_83532]) ).

tcf(c_109535,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_108992,c_83524]) ).

tcf(c_109536,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_108992]) ).

tcf(c_109537,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_107183]) ).

tcf(c_109541,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_106960]) ).

tcf(c_109542,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_105967]) ).

tcf(c_109544,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_95608]) ).

tcf(c_109547,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_108992,c_98014]) ).

tcf(c_109548,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_95414]) ).

tcf(c_109549,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_95286]) ).

tcf(c_109550,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_95041]) ).

tcf(c_109551,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_94695]) ).

tcf(c_109552,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_94594]) ).

tcf(c_109553,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_93822]) ).

tcf(c_109554,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_93551]) ).

tcf(c_109555,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108992,c_79918]) ).

tcf(c_109558,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108992,c_83537]) ).

tcf(c_109559,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108992,c_83534]) ).

tcf(c_109564,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108992,c_96186]) ).

tcf(c_109565,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109487,c_59636]) ).

tcf(c_109566,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109482,c_79190]) ).

tcf(c_109567,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109555,c_76415]) ).

tcf(c_109568,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109490,c_76855,c_93903]) ).

tcf(c_109572,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_109547,c_79573]) ).

tcf(c_109636,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_92656]) ).

tcf(c_109637,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_108926,c_255]) ).

tcf(c_109639,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108926,c_256]) ).

tcf(c_109641,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_108926,c_83532]) ).

tcf(c_109642,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_108926,c_83524]) ).

tcf(c_109643,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_108992]) ).

tcf(c_109644,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_107183]) ).

tcf(c_109648,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_106960]) ).

tcf(c_109649,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_105967]) ).

tcf(c_109651,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_95608]) ).

tcf(c_109654,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_108926,c_98014]) ).

tcf(c_109655,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_95414]) ).

tcf(c_109656,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_95286]) ).

tcf(c_109657,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_95041]) ).

tcf(c_109658,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_94695]) ).

tcf(c_109659,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_94594]) ).

tcf(c_109660,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_93822]) ).

tcf(c_109661,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_93551]) ).

tcf(c_109662,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108926,c_79918]) ).

tcf(c_109665,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108926,c_83537]) ).

tcf(c_109666,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108926,c_83534]) ).

tcf(c_109671,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_108926,c_96186]) ).

tcf(c_109678,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_109654,c_79573]) ).

tcf(c_109696,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_109567]) ).

tcf(c_109697,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_109567]) ).

tcf(c_109698,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_109567]) ).

tcf(c_109699,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_109567]) ).

tcf(c_109701,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_109567]) ).

tcf(c_109702,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_109567]) ).

tcf(c_109704,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_109567]) ).

tcf(c_109705,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_109567]) ).

tcf(c_109706,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_109567]) ).

tcf(c_109707,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_109567]) ).

tcf(c_109708,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_109567]) ).

tcf(c_109709,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_109567]) ).

tcf(c_109710,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_109567]) ).

tcf(c_109711,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_109567]) ).

tcf(c_109712,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_109567]) ).

tcf(c_109713,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_109567]) ).

tcf(c_109714,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_109567]) ).

tcf(c_109715,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_109567]) ).

tcf(c_109716,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_109567]) ).

tcf(c_109717,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_109567]) ).

tcf(c_109718,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_109567]) ).

tcf(c_109719,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_109567]) ).

tcf(c_109720,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_109567]) ).

tcf(c_109721,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_109567]) ).

tcf(c_109722,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_109567]) ).

tcf(c_109723,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_109567]) ).

tcf(c_109724,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_109567]) ).

tcf(c_109725,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_109567]) ).

tcf(c_109726,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_109567]) ).

tcf(c_109727,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_109567]) ).

tcf(c_109728,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_109567]) ).

tcf(c_109729,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_109567]) ).

tcf(c_109730,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_109567]) ).

tcf(c_109731,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_109567]) ).

tcf(c_109732,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_109567]) ).

tcf(c_109733,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_109567]) ).

tcf(c_109734,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_109567]) ).

tcf(c_109735,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_109567]) ).

tcf(c_109736,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_109567]) ).

tcf(c_109737,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_109567]) ).

tcf(c_109738,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_109567]) ).

tcf(c_109739,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_109567]) ).

tcf(c_109740,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_109567]) ).

tcf(c_109741,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_109567]) ).

tcf(c_109742,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_109567]) ).

tcf(c_109745,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_92656]) ).

tcf(c_109746,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_109567,c_255]) ).

tcf(c_109748,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109567,c_256]) ).

tcf(c_109750,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_109567,c_83532]) ).

tcf(c_109751,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_109567,c_83524]) ).

tcf(c_109752,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_109567]) ).

tcf(c_109753,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_108992]) ).

tcf(c_109754,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_107183]) ).

tcf(c_109758,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_106960]) ).

tcf(c_109759,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_105967]) ).

tcf(c_109761,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_95608]) ).

tcf(c_109764,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_109567,c_98014]) ).

tcf(c_109765,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_95414]) ).

tcf(c_109766,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_95286]) ).

tcf(c_109767,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_95041]) ).

tcf(c_109768,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_94695]) ).

tcf(c_109769,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_94594]) ).

tcf(c_109770,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_93822]) ).

tcf(c_109771,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_93551]) ).

tcf(c_109772,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109567,c_79918]) ).

tcf(c_109775,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109567,c_83537]) ).

tcf(c_109776,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109567,c_83534]) ).

tcf(c_109781,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109567,c_96186]) ).

tcf(c_109782,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109701,c_59636]) ).

tcf(c_109783,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109696,c_79190]) ).

tcf(c_109784,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109772,c_76415]) ).

tcf(c_109785,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_109704,c_76855,c_93903]) ).

tcf(c_109789,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_109764,c_79573]) ).

tcf(c_109896,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),
    inference(superposition,[status(thm)],[c_59636,c_98911]) ).

tcf(c_109898,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),m))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_99039,c_98911]) ).

tcf(c_109901,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(m),X1)))),
    inference(superposition,[status(thm)],[c_79557,c_98911]) ).

tcf(c_109902,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79437,c_98911]) ).

tcf(c_109903,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X1))),
    inference(superposition,[status(thm)],[c_99171,c_98911]) ).

tcf(c_109904,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),X1))),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_103848,c_98911]) ).

tcf(c_109905,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(m),X1)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_98911]) ).

tcf(c_109910,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(pls)),
    inference(superposition,[status(thm)],[c_1001,c_98911]) ).

tcf(c_109918,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m)),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X1)),m)),X2))),
    inference(superposition,[status(thm)],[c_93890,c_98911]) ).

tcf(c_109919,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X1),X1)))),X2))),
    inference(superposition,[status(thm)],[c_78930,c_98911]) ).

tcf(c_109920,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_15)),X1))),
    inference(superposition,[status(thm)],[c_78938,c_98911]) ).

tcf(c_109921,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X1))),
    inference(superposition,[status(thm)],[c_79190,c_98911]) ).

tcf(c_109922,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X1)))),X2))),
    inference(superposition,[status(thm)],[c_79161,c_98911]) ).

tcf(c_109923,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X1),iPr_def_14)))),X2))),
    inference(superposition,[status(thm)],[c_79901,c_98911]) ).

tcf(c_109924,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))),X1))),
    inference(superposition,[status(thm)],[c_79904,c_98911]) ).

tcf(c_109925,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(m),X1))),
    inference(superposition,[status(thm)],[c_83594,c_98911]) ).

tcf(c_109927,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))),
    inference(superposition,[status(thm)],[c_85658,c_98911]) ).

tcf(c_109928,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X1))),
    inference(superposition,[status(thm)],[c_88494,c_98911]) ).

tcf(c_109929,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))),X2))),
    inference(superposition,[status(thm)],[c_88513,c_98911]) ).

tcf(c_109930,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),X2))),
    inference(superposition,[status(thm)],[c_88550,c_98911]) ).

tcf(c_109955,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),X2))),
    inference(superposition,[status(thm)],[c_107289,c_98911]) ).

tcf(c_109956,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1))),
    inference(superposition,[status(thm)],[c_108926,c_98911]) ).

tcf(c_109960,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_92656]) ).

tcf(c_109961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X0)),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X3),
    inference(superposition,[status(thm)],[c_98911,c_255]) ).

tcf(c_109962,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_98911,c_76880]) ).

tcf(c_109963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))),
    inference(superposition,[status(thm)],[c_98911,c_256]) ).

tcf(c_109965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3)))),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X2)),X3))),
    inference(superposition,[status(thm)],[c_98911,c_255]) ).

tcf(c_109966,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_109567]) ).

tcf(c_109967,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_108992]) ).

tcf(c_109968,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_107183]) ).

tcf(c_109969,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2))),
    inference(superposition,[status(thm)],[c_98911,c_98916]) ).

tcf(c_109970,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2))),
    inference(superposition,[status(thm)],[c_98911,c_98914]) ).

tcf(c_109971,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2))),
    inference(superposition,[status(thm)],[c_98911,c_98913]) ).

tcf(c_109972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_106960]) ).

tcf(c_109973,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_105967]) ).

tcf(c_109974,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2))),
    inference(superposition,[status(thm)],[c_98911,c_106496]) ).

tcf(c_109975,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_95608]) ).

tcf(c_109976,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_98911,c_99891]) ).

tcf(c_109978,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X0))),
    inference(superposition,[status(thm)],[c_98911,c_98014]) ).

tcf(c_109979,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_95414]) ).

tcf(c_109980,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_95286]) ).

tcf(c_109981,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_95041]) ).

tcf(c_109982,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_94695]) ).

tcf(c_109983,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_94594]) ).

tcf(c_109984,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_93822]) ).

tcf(c_109985,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_93551]) ).

tcf(c_109986,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_98911,c_79918]) ).

tcf(c_109987,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),X2)))),
    inference(superposition,[status(thm)],[c_98911,c_98897]) ).

tcf(c_109990,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X2))) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),
    inference(superposition,[status(thm)],[c_98911,c_92625]) ).

tcf(c_109991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X3)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X3))),
    inference(superposition,[status(thm)],[c_98911,c_98911]) ).

tcf(c_109992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X3))))),X0) = pls,
    inference(superposition,[status(thm)],[c_98911,c_98912]) ).

tcf(c_109993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),X3)))),
    inference(superposition,[status(thm)],[c_98911,c_98882]) ).

tcf(c_109994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))),X3))))),
    inference(superposition,[status(thm)],[c_98911,c_98875]) ).

tcf(c_109995,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))))),
    inference(superposition,[status(thm)],[c_98911,c_98873]) ).

tcf(c_109996,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls),
    inference(light_normalisation,[status(thm)],[c_109910,c_574]) ).

tcf(c_109997,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))))),
    inference(light_normalisation,[status(thm)],[c_109987,c_98105]) ).

tcf(c_109998,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,X1))),
    inference(light_normalisation,[status(thm)],[c_109925,c_59637]) ).

tcf(c_109999,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2)))),
    inference(light_normalisation,[status(thm)],[c_109974,c_98105]) ).

tcf(c_110000,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2)))),
    inference(light_normalisation,[status(thm)],[c_109971,c_98105]) ).

tcf(c_110001,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2)))),
    inference(light_normalisation,[status(thm)],[c_109970,c_98105]) ).

tcf(c_110002,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),X2)))),
    inference(light_normalisation,[status(thm)],[c_109969,c_98105]) ).

tcf(c_110209,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),one_one_int)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_59636,c_99037]) ).

tcf(c_110214,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),m))),sK30(iPr_def_19)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),m))),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_79573,c_99037]) ).

tcf(c_110215,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_79414,c_99037]) ).

tcf(c_110216,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_99171,c_99037]) ).

tcf(c_110217,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),m)),iPr_def_11)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),m)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_82861,c_99037]) ).

tcf(c_110222,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),m))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X1),m)))),
    inference(superposition,[status(thm)],[c_59637,c_99037]) ).

tcf(c_110226,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),m)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),m))),
    inference(superposition,[status(thm)],[c_77148,c_99037]) ).

tcf(c_110227,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_13,iPr_def_14))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(iPr_def_13,iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79190,c_99037]) ).

tcf(c_110230,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_92656]) ).

tcf(c_110231,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X0)),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X3),
    inference(superposition,[status(thm)],[c_99037,c_255]) ).

tcf(c_110232,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_99037,c_76880]) ).

tcf(c_110233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))),
    inference(superposition,[status(thm)],[c_99037,c_256]) ).

tcf(c_110235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m))))),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X2),hAPP_int_int(plus_plus_int(X3),m)))),
    inference(superposition,[status(thm)],[c_99037,c_255]) ).

tcf(c_110236,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_109567]) ).

tcf(c_110237,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_108992]) ).

tcf(c_110238,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_107183]) ).

tcf(c_110239,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2))),
    inference(superposition,[status(thm)],[c_99037,c_98916]) ).

tcf(c_110240,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2))),
    inference(superposition,[status(thm)],[c_99037,c_98914]) ).

tcf(c_110241,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2))),
    inference(superposition,[status(thm)],[c_99037,c_98913]) ).

tcf(c_110242,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_106960]) ).

tcf(c_110243,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_105967]) ).

tcf(c_110244,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2))),
    inference(superposition,[status(thm)],[c_99037,c_106496]) ).

tcf(c_110245,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_95608]) ).

tcf(c_110246,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_99037,c_99891]) ).

tcf(c_110248,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X0))),
    inference(superposition,[status(thm)],[c_99037,c_98014]) ).

tcf(c_110249,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_95414]) ).

tcf(c_110250,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_95286]) ).

tcf(c_110251,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_95041]) ).

tcf(c_110252,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_94695]) ).

tcf(c_110253,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_94594]) ).

tcf(c_110254,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_93822]) ).

tcf(c_110255,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_93551]) ).

tcf(c_110256,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m))) = number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_99037,c_79918]) ).

tcf(c_110257,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),X2)))),
    inference(superposition,[status(thm)],[c_99037,c_98897]) ).

tcf(c_110260,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X2))) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),
    inference(superposition,[status(thm)],[c_99037,c_92625]) ).

tcf(c_110261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X3)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X3))),
    inference(superposition,[status(thm)],[c_99037,c_98911]) ).

tcf(c_110262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X3))))),X0) = pls,
    inference(superposition,[status(thm)],[c_99037,c_98912]) ).

tcf(c_110263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),X3)))),
    inference(superposition,[status(thm)],[c_99037,c_98882]) ).

tcf(c_110264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))),X3))))),
    inference(superposition,[status(thm)],[c_99037,c_98875]) ).

tcf(c_110265,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))))),
    inference(superposition,[status(thm)],[c_99037,c_98873]) ).

tcf(c_110266,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))))),
    inference(light_normalisation,[status(thm)],[c_110257,c_98072]) ).

tcf(c_110267,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)))),
    inference(light_normalisation,[status(thm)],[c_110244,c_98072]) ).

tcf(c_110268,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)))),
    inference(light_normalisation,[status(thm)],[c_110241,c_98072]) ).

tcf(c_110269,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)))),
    inference(light_normalisation,[status(thm)],[c_110240,c_98072]) ).

tcf(c_110270,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2))))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),X2)))),
    inference(light_normalisation,[status(thm)],[c_110239,c_98072]) ).

tcf(c_110344,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_107331,c_253]) ).

tcf(c_110346,plain,
    hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_59636,c_110344]) ).

tcf(c_110348,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_92656]) ).

tcf(c_110349,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1),
    inference(superposition,[status(thm)],[c_110344,c_255]) ).

tcf(c_110351,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_110344,c_256]) ).

tcf(c_110353,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(plus_plus_int(X0),X1)))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_110344,c_255]) ).

tcf(c_110354,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_109567]) ).

tcf(c_110355,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_108992]) ).

tcf(c_110356,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_107183]) ).

tcf(c_110357,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_110344,c_98916]) ).

tcf(c_110358,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),one_one_nat) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_110344,c_98914]) ).

tcf(c_110359,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),pls) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_110344,c_98913]) ).

tcf(c_110360,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_106960]) ).

tcf(c_110361,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_105967]) ).

tcf(c_110362,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_110344,c_106496]) ).

tcf(c_110363,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_95608]) ).

tcf(c_110364,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),iPr_def_11))),
    inference(superposition,[status(thm)],[c_110344,c_99891]) ).

tcf(c_110366,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0))),
    inference(superposition,[status(thm)],[c_110344,c_98014]) ).

tcf(c_110367,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_95414]) ).

tcf(c_110368,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_95286]) ).

tcf(c_110369,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_95041]) ).

tcf(c_110370,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_94695]) ).

tcf(c_110371,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_94594]) ).

tcf(c_110372,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_93822]) ).

tcf(c_110373,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_93551]) ).

tcf(c_110374,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m))) = number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_110344,c_79918]) ).

tcf(c_110375,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)))),
    inference(superposition,[status(thm)],[c_110344,c_98897]) ).

tcf(c_110376,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_110344,c_93345]) ).

tcf(c_110377,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_110344,c_92614]) ).

tcf(c_110378,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_110344,c_92625]) ).

tcf(c_110379,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1)))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))),
    inference(superposition,[status(thm)],[c_110344,c_98911]) ).

tcf(c_110380,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))))),X0) = pls,
    inference(superposition,[status(thm)],[c_110344,c_98912]) ).

tcf(c_110381,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),X1)))),
    inference(superposition,[status(thm)],[c_110344,c_98882]) ).

tcf(c_110382,plain,
    ! [X0: $i,X1: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X1))))),
    inference(superposition,[status(thm)],[c_110344,c_98875]) ).

tcf(c_110383,plain,
    ! [X0: $i] : is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))),
    inference(superposition,[status(thm)],[c_110344,c_98873]) ).

tcf(c_110424,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_92656]) ).

tcf(c_110425,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_109498,c_255]) ).

tcf(c_110427,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109498,c_256]) ).

tcf(c_110429,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_109498,c_83532]) ).

tcf(c_110430,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_109498,c_83524]) ).

tcf(c_110431,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_109567]) ).

tcf(c_110432,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_108992]) ).

tcf(c_110433,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_107183]) ).

tcf(c_110437,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_106960]) ).

tcf(c_110438,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_105967]) ).

tcf(c_110440,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_95608]) ).

tcf(c_110443,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_109498,c_98014]) ).

tcf(c_110444,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_95414]) ).

tcf(c_110445,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_95286]) ).

tcf(c_110446,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_95041]) ).

tcf(c_110447,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_94695]) ).

tcf(c_110448,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_94594]) ).

tcf(c_110449,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_93822]) ).

tcf(c_110450,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_93551]) ).

tcf(c_110451,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109498,c_79918]) ).

tcf(c_110454,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109498,c_83537]) ).

tcf(c_110455,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109498,c_83534]) ).

tcf(c_110461,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109498,c_96186]) ).

tcf(c_110468,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_110443,c_79573]) ).

tcf(c_110496,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_109784]) ).

tcf(c_110497,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_109784]) ).

tcf(c_110498,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_109784]) ).

tcf(c_110499,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_109784]) ).

tcf(c_110501,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_109784]) ).

tcf(c_110502,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_109784]) ).

tcf(c_110504,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_109784]) ).

tcf(c_110505,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_109784]) ).

tcf(c_110506,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_109784]) ).

tcf(c_110507,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_109784]) ).

tcf(c_110508,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_109784]) ).

tcf(c_110509,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_109784]) ).

tcf(c_110510,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_109784]) ).

tcf(c_110511,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_109784]) ).

tcf(c_110512,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_109784]) ).

tcf(c_110513,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_109784]) ).

tcf(c_110514,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_109784]) ).

tcf(c_110515,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_109784]) ).

tcf(c_110516,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_109784]) ).

tcf(c_110517,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_109784]) ).

tcf(c_110518,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_109784]) ).

tcf(c_110519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_109784]) ).

tcf(c_110520,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_109784]) ).

tcf(c_110521,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_109784]) ).

tcf(c_110522,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_109784]) ).

tcf(c_110523,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_109784]) ).

tcf(c_110524,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_109784]) ).

tcf(c_110525,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_109784]) ).

tcf(c_110526,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_109784]) ).

tcf(c_110527,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_109784]) ).

tcf(c_110528,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_109784]) ).

tcf(c_110529,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_109784]) ).

tcf(c_110530,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_109784]) ).

tcf(c_110531,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_109784]) ).

tcf(c_110532,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_109784]) ).

tcf(c_110533,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_109784]) ).

tcf(c_110534,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_109784]) ).

tcf(c_110535,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_109784]) ).

tcf(c_110536,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_109784]) ).

tcf(c_110537,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_109784]) ).

tcf(c_110538,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_109784]) ).

tcf(c_110539,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_109784]) ).

tcf(c_110540,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_109784]) ).

tcf(c_110541,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_109784]) ).

tcf(c_110542,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_109784]) ).

tcf(c_110543,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_109784]) ).

tcf(c_110544,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_109784]) ).

tcf(c_110545,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_109784]) ).

tcf(c_110546,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_109784]) ).

tcf(c_110548,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_109784]) ).

tcf(c_110550,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_92656]) ).

tcf(c_110551,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_109784,c_255]) ).

tcf(c_110553,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109784,c_256]) ).

tcf(c_110555,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_109784,c_83532]) ).

tcf(c_110556,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_109784,c_83524]) ).

tcf(c_110557,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_109784]) ).

tcf(c_110558,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_109567]) ).

tcf(c_110559,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_108992]) ).

tcf(c_110560,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_107183]) ).

tcf(c_110564,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_106960]) ).

tcf(c_110565,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_105967]) ).

tcf(c_110567,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_95608]) ).

tcf(c_110570,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_109784,c_98014]) ).

tcf(c_110571,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_95414]) ).

tcf(c_110572,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_95286]) ).

tcf(c_110573,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_95041]) ).

tcf(c_110574,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_94695]) ).

tcf(c_110575,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_94594]) ).

tcf(c_110576,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_93822]) ).

tcf(c_110577,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_93551]) ).

tcf(c_110578,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109784,c_79918]) ).

tcf(c_110581,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109784,c_83537]) ).

tcf(c_110582,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109784,c_83534]) ).

tcf(c_110588,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109784,c_96186]) ).

tcf(c_110589,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110501,c_59636]) ).

tcf(c_110590,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110496,c_79190]) ).

tcf(c_110591,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110578,c_76415]) ).

tcf(c_110592,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110504,c_76855,c_93903]) ).

tcf(c_110596,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_110570,c_79573]) ).

tcf(c_110697,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),min),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(light_normalisation,[status(thm)],[c_1518,c_76397]) ).

tcf(c_110704,plain,
    ( hBOOL(hAPP_int_bool(zcong(zfact(min),min),pls))
    | ~ hBOOL(hAPP_int_bool(zprime,pls)) ),
    inference(superposition,[status(thm)],[c_78632,c_110697]) ).

tcf(c_110705,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(X0,zcong(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),min)))
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(superposition,[status(thm)],[c_110697,c_226]) ).

tcf(c_110706,plain,
    ! [X0: $i] :
      ( is_int(sK14(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),min,X0))
      | ~ is_int(min)
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(superposition,[status(thm)],[c_110697,c_852]) ).

tcf(c_110707,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(min,zfact(hAPP_int_int(minus_minus_int(X0),one_one_int))),X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(superposition,[status(thm)],[c_110697,c_814]) ).

tcf(c_110708,plain,
    ( hBOOL(hAPP_int_bool(zcong(one_one_int,min),pls))
    | ~ hBOOL(hAPP_int_bool(zprime,pls)) ),
    inference(light_normalisation,[status(thm)],[c_110704,c_78655]) ).

tcf(c_110715,plain,
    ! [X0: $i] :
      ( is_int(sK14(zfact(hAPP_int_int(minus_minus_int(X0),one_one_int)),min,X0))
      | ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_110706,c_56]) ).

tcf(c_110731,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X0)))
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),sK36(number_number_of_nat(X0),number_number_of_nat(X1))) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_131,c_1583]) ).

tcf(c_110732,plain,
    ! [X0: $i] :
      ( ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,X0)) = X0 ) ),
    inference(superposition,[status(thm)],[c_1316,c_1583]) ).

tcf(c_110734,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,hAPP_nat_nat(power_power_nat(X0),X1))) = hAPP_nat_nat(power_power_nat(X0),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_741,c_1583]) ).

tcf(c_110735,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,number_number_of_nat(X0))) = number_number_of_nat(X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45950,c_1583]) ).

tcf(c_110736,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,hAPP_nat_nat(plus_plus_nat(X2),X1))) = hAPP_nat_nat(plus_plus_nat(X2),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1348,c_1583]) ).

tcf(c_110737,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X1),sK36(X1,X0)) = X0 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1583]) ).

tcf(c_110738,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( X0 = X1 )
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,X1)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1583]) ).

tcf(c_110739,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),sK36(hAPP_nat_nat(minus_minus_nat(X0),X2),X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1262,c_1583]) ).

tcf(c_110740,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,hAPP_nat_nat(minus_minus_nat(X1),X0))) = hAPP_nat_nat(minus_minus_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1319,c_1583]) ).

tcf(c_110741,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,hAPP_nat_nat(plus_plus_nat(X1),X2))) = hAPP_nat_nat(plus_plus_nat(X1),X2) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1347,c_1583]) ).

tcf(c_110742,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
      | ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0)))) = sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1583]) ).

tcf(c_110743,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,sK36(X0,X1))) = sK36(X0,X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1582,c_1583]) ).

tcf(c_110744,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X1),sK36(X1,hAPP_nat_nat(div_mod_nat(X0),X2))) = hAPP_nat_nat(div_mod_nat(X0),X2) )
      | ~ sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1583]) ).

tcf(c_110745,plain,
    hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,one_one_nat)) = one_one_nat,
    inference(superposition,[status(thm)],[c_11147,c_1583]) ).

tcf(c_110746,plain,
    hAPP_nat_nat(plus_plus_nat(zero_zero_nat),sK36(zero_zero_nat,iPr_def_11)) = iPr_def_11,
    inference(superposition,[status(thm)],[c_76735,c_1583]) ).

tcf(c_110747,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,hAPP_nat_nat(iPr_def_10,X0))) = hAPP_nat_nat(iPr_def_10,X0),
    inference(superposition,[status(thm)],[c_102906,c_1583]) ).

tcf(c_110748,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),sK36(one_one_nat,iPr_def_11)) = iPr_def_11,
    inference(superposition,[status(thm)],[c_102905,c_1583]) ).

tcf(c_110749,plain,
    hAPP_nat_nat(iPr_def_10,sK36(one_one_nat,iPr_def_11)) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_110748,c_59634]) ).

tcf(c_110775,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(X0),sK36(X0,sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0)))) = sK35(X1,hAPP_n1699378549t_bool(ord_less_nat,X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_110742,c_1317]) ).

tcf(c_110811,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,hAPP_int_int(div_mod_int(X0),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_59643,c_1643]) ).

tcf(c_110830,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(X0),X1)),X1)) ),
    inference(superposition,[status(thm)],[c_1643,c_46112]) ).

tcf(c_110831,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(member_int(hAPP_int_int(div_mod_int(X0),X1),d22set(X1))) ),
    inference(superposition,[status(thm)],[c_1643,c_1579]) ).

tcf(c_110832,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(div_mod_int(X1),X0),hAPP_i1948725293t_bool(ord_less_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_1643,c_226]) ).

tcf(c_110833,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(div_mod_int(X0),pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
    inference(superposition,[status(thm)],[c_1643,c_611]) ).

tcf(c_110847,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_77670,c_1682]) ).

tcf(c_110850,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(div_mod_nat(X1),X0)),sK18(hAPP_nat_nat(div_mod_nat(X1),X0),X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1682,c_1376]) ).

tcf(c_110851,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(div_mod_nat(X1),X0)),X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1682,c_1332]) ).

tcf(c_110852,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(X0),zero_zero_nat) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1682,c_1329]) ).

tcf(c_110854,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X1))),X1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(div_mod_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1682,c_1712]) ).

tcf(c_110865,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK36(one_one_nat,iPr_def_11)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_110749,c_102906]) ).

tcf(c_110866,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),sK36(one_one_nat,iPr_def_11))),
    inference(superposition,[status(thm)],[c_110749,c_77614]) ).

tcf(c_110869,plain,
    hAPP_nat_nat(minus_minus_nat(iPr_def_11),one_one_nat) = sK36(one_one_nat,iPr_def_11),
    inference(superposition,[status(thm)],[c_110749,c_77549]) ).

tcf(c_110870,plain,
    hAPP_nat_nat(minus_minus_nat(iPr_def_11),sK36(one_one_nat,iPr_def_11)) = one_one_nat,
    inference(superposition,[status(thm)],[c_110749,c_77538]) ).

tcf(c_110871,plain,
    sK36(one_one_nat,iPr_def_11) != iPr_def_11,
    inference(superposition,[status(thm)],[c_110749,c_78756]) ).

tcf(c_110876,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK36(one_one_nat,iPr_def_11)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_110749,c_76584]) ).

tcf(c_110877,plain,
    sK36(one_one_nat,iPr_def_11) = one_one_nat,
    inference(light_normalisation,[status(thm)],[c_110869,c_78900]) ).

tcf(c_110883,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_92656]) ).

tcf(c_110884,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_109712,c_255]) ).

tcf(c_110886,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109712,c_256]) ).

tcf(c_110888,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_109712,c_83532]) ).

tcf(c_110889,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_109712,c_83524]) ).

tcf(c_110890,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_109784]) ).

tcf(c_110891,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_109567]) ).

tcf(c_110892,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_108992]) ).

tcf(c_110893,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_107183]) ).

tcf(c_110897,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_106960]) ).

tcf(c_110898,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_105967]) ).

tcf(c_110900,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_95608]) ).

tcf(c_110903,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_109712,c_98014]) ).

tcf(c_110904,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_95414]) ).

tcf(c_110905,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_95286]) ).

tcf(c_110906,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_95041]) ).

tcf(c_110907,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_94695]) ).

tcf(c_110908,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_94594]) ).

tcf(c_110909,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_93822]) ).

tcf(c_110910,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_93551]) ).

tcf(c_110911,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109712,c_79918]) ).

tcf(c_110914,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109712,c_83537]) ).

tcf(c_110915,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109712,c_83534]) ).

tcf(c_110921,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_109712,c_96186]) ).

tcf(c_110928,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_110903,c_79573]) ).

tcf(c_110981,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_110591]) ).

tcf(c_110982,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_110591]) ).

tcf(c_110983,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_110591]) ).

tcf(c_110984,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_110591]) ).

tcf(c_110986,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_110591]) ).

tcf(c_110987,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_110591]) ).

tcf(c_110989,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_110591]) ).

tcf(c_110990,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_110591]) ).

tcf(c_110991,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_110591]) ).

tcf(c_110992,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_110591]) ).

tcf(c_110993,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_110591]) ).

tcf(c_110994,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_110591]) ).

tcf(c_110995,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_110591]) ).

tcf(c_110996,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_110591]) ).

tcf(c_110997,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_110591]) ).

tcf(c_110998,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_110591]) ).

tcf(c_110999,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_110591]) ).

tcf(c_111000,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_110591]) ).

tcf(c_111001,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_110591]) ).

tcf(c_111002,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_110591]) ).

tcf(c_111003,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_110591]) ).

tcf(c_111004,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_110591]) ).

tcf(c_111005,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_110591]) ).

tcf(c_111006,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_110591]) ).

tcf(c_111007,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_110591]) ).

tcf(c_111008,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_110591]) ).

tcf(c_111009,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_110591]) ).

tcf(c_111010,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_110591]) ).

tcf(c_111011,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_110591]) ).

tcf(c_111012,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_110591]) ).

tcf(c_111013,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_110591]) ).

tcf(c_111014,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_110591]) ).

tcf(c_111015,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_110591]) ).

tcf(c_111016,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_110591]) ).

tcf(c_111017,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_110591]) ).

tcf(c_111018,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_110591]) ).

tcf(c_111019,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_110591]) ).

tcf(c_111020,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_110591]) ).

tcf(c_111021,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_110591]) ).

tcf(c_111022,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_110591]) ).

tcf(c_111023,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_110591]) ).

tcf(c_111024,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_110591]) ).

tcf(c_111025,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_110591]) ).

tcf(c_111026,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_110591]) ).

tcf(c_111027,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_110591]) ).

tcf(c_111028,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_110591]) ).

tcf(c_111029,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_110591]) ).

tcf(c_111030,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_110591]) ).

tcf(c_111031,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_110591]) ).

tcf(c_111032,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_110591]) ).

tcf(c_111033,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_110591]) ).

tcf(c_111034,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_110591]) ).

tcf(c_111037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_92656]) ).

tcf(c_111038,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_110591,c_255]) ).

tcf(c_111040,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110591,c_256]) ).

tcf(c_111042,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_110591,c_83532]) ).

tcf(c_111043,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_110591,c_83524]) ).

tcf(c_111044,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_110591]) ).

tcf(c_111045,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_109784]) ).

tcf(c_111046,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_109567]) ).

tcf(c_111047,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_108992]) ).

tcf(c_111048,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_107183]) ).

tcf(c_111052,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_106960]) ).

tcf(c_111053,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_105967]) ).

tcf(c_111055,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_95608]) ).

tcf(c_111058,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_110591,c_98014]) ).

tcf(c_111059,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_95414]) ).

tcf(c_111060,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_95286]) ).

tcf(c_111061,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_95041]) ).

tcf(c_111062,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_94695]) ).

tcf(c_111063,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_94594]) ).

tcf(c_111064,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_93822]) ).

tcf(c_111065,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_93551]) ).

tcf(c_111066,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110591,c_79918]) ).

tcf(c_111069,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110591,c_83537]) ).

tcf(c_111070,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110591,c_83534]) ).

tcf(c_111076,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110591,c_96186]) ).

tcf(c_111077,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110986,c_59636]) ).

tcf(c_111078,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110981,c_79190]) ).

tcf(c_111079,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111066,c_76415]) ).

tcf(c_111080,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_110989,c_76855,c_93903]) ).

tcf(c_111084,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111058,c_79573]) ).

tcf(c_111224,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_92656]) ).

tcf(c_111225,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_110512,c_255]) ).

tcf(c_111227,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110512,c_256]) ).

tcf(c_111229,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_110512,c_83532]) ).

tcf(c_111230,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_110512,c_83524]) ).

tcf(c_111231,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_110591]) ).

tcf(c_111232,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_109784]) ).

tcf(c_111233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_109567]) ).

tcf(c_111234,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_108992]) ).

tcf(c_111235,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_107183]) ).

tcf(c_111239,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_106960]) ).

tcf(c_111240,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_105967]) ).

tcf(c_111242,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_95608]) ).

tcf(c_111245,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_110512,c_98014]) ).

tcf(c_111246,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_95414]) ).

tcf(c_111247,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_95286]) ).

tcf(c_111248,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_95041]) ).

tcf(c_111249,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_94695]) ).

tcf(c_111250,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_94594]) ).

tcf(c_111251,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_93822]) ).

tcf(c_111252,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_93551]) ).

tcf(c_111253,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110512,c_79918]) ).

tcf(c_111256,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110512,c_83537]) ).

tcf(c_111257,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110512,c_83534]) ).

tcf(c_111263,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110512,c_96186]) ).

tcf(c_111270,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111245,c_79573]) ).

tcf(c_111304,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_111079]) ).

tcf(c_111305,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_111079]) ).

tcf(c_111306,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_111079]) ).

tcf(c_111307,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_111079]) ).

tcf(c_111309,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_111079]) ).

tcf(c_111310,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_111079]) ).

tcf(c_111312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_111079]) ).

tcf(c_111313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_111079]) ).

tcf(c_111314,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_111079]) ).

tcf(c_111315,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_111079]) ).

tcf(c_111316,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_111079]) ).

tcf(c_111317,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_111079]) ).

tcf(c_111318,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_111079]) ).

tcf(c_111319,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_111079]) ).

tcf(c_111320,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_111079]) ).

tcf(c_111321,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_111079]) ).

tcf(c_111322,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_111079]) ).

tcf(c_111323,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_111079]) ).

tcf(c_111324,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_111079]) ).

tcf(c_111325,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_111079]) ).

tcf(c_111326,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_111079]) ).

tcf(c_111327,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_111079]) ).

tcf(c_111328,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_111079]) ).

tcf(c_111329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_111079]) ).

tcf(c_111330,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_111079]) ).

tcf(c_111331,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_111079]) ).

tcf(c_111332,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_111079]) ).

tcf(c_111333,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_111079]) ).

tcf(c_111334,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_111079]) ).

tcf(c_111335,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_111079]) ).

tcf(c_111336,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_111079]) ).

tcf(c_111337,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_111079]) ).

tcf(c_111338,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_111079]) ).

tcf(c_111339,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_111079]) ).

tcf(c_111340,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_111079]) ).

tcf(c_111341,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_111079]) ).

tcf(c_111342,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_111079]) ).

tcf(c_111343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_111079]) ).

tcf(c_111344,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_111079]) ).

tcf(c_111345,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_111079]) ).

tcf(c_111346,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_111079]) ).

tcf(c_111347,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_111079]) ).

tcf(c_111348,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_111079]) ).

tcf(c_111349,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_111079]) ).

tcf(c_111350,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_111079]) ).

tcf(c_111351,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_111079]) ).

tcf(c_111352,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_111079]) ).

tcf(c_111353,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_111079]) ).

tcf(c_111354,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_111079]) ).

tcf(c_111355,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_111079]) ).

tcf(c_111356,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_111079]) ).

tcf(c_111357,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_111079]) ).

tcf(c_111358,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_111079]) ).

tcf(c_111359,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_111079]) ).

tcf(c_111362,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_92656]) ).

tcf(c_111363,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_111079,c_255]) ).

tcf(c_111365,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111079,c_256]) ).

tcf(c_111367,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111079,c_83532]) ).

tcf(c_111368,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111079,c_83524]) ).

tcf(c_111369,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_111079]) ).

tcf(c_111370,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_110591]) ).

tcf(c_111371,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_109784]) ).

tcf(c_111372,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_109567]) ).

tcf(c_111373,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_108992]) ).

tcf(c_111374,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_107183]) ).

tcf(c_111378,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_106960]) ).

tcf(c_111379,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_105967]) ).

tcf(c_111381,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_95608]) ).

tcf(c_111384,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111079,c_98014]) ).

tcf(c_111385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_95414]) ).

tcf(c_111386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_95286]) ).

tcf(c_111387,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_95041]) ).

tcf(c_111388,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_94695]) ).

tcf(c_111389,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_94594]) ).

tcf(c_111390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_93822]) ).

tcf(c_111391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_93551]) ).

tcf(c_111392,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111079,c_79918]) ).

tcf(c_111395,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111079,c_83537]) ).

tcf(c_111396,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111079,c_83534]) ).

tcf(c_111402,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111079,c_96186]) ).

tcf(c_111403,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111309,c_59636]) ).

tcf(c_111404,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111304,c_79190]) ).

tcf(c_111405,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111392,c_76415]) ).

tcf(c_111406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111312,c_76855,c_93903]) ).

tcf(c_111410,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111384,c_79573]) ).

tcf(c_111606,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_92656]) ).

tcf(c_111607,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_110997,c_255]) ).

tcf(c_111609,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110997,c_256]) ).

tcf(c_111611,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_110997,c_83532]) ).

tcf(c_111612,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_110997,c_83524]) ).

tcf(c_111613,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_111079]) ).

tcf(c_111614,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_110591]) ).

tcf(c_111615,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_109784]) ).

tcf(c_111616,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_109567]) ).

tcf(c_111617,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_108992]) ).

tcf(c_111618,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_107183]) ).

tcf(c_111622,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_106960]) ).

tcf(c_111623,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_105967]) ).

tcf(c_111625,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_95608]) ).

tcf(c_111628,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_110997,c_98014]) ).

tcf(c_111629,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_95414]) ).

tcf(c_111630,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_95286]) ).

tcf(c_111631,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_95041]) ).

tcf(c_111632,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_94695]) ).

tcf(c_111633,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_94594]) ).

tcf(c_111634,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_93822]) ).

tcf(c_111635,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_93551]) ).

tcf(c_111636,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110997,c_79918]) ).

tcf(c_111639,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110997,c_83537]) ).

tcf(c_111640,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110997,c_83534]) ).

tcf(c_111646,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_110997,c_96186]) ).

tcf(c_111653,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111628,c_79573]) ).

tcf(c_111663,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_111405]) ).

tcf(c_111664,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_111405]) ).

tcf(c_111665,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_111405]) ).

tcf(c_111666,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_111405]) ).

tcf(c_111668,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_111405]) ).

tcf(c_111669,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_111405]) ).

tcf(c_111671,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_111405]) ).

tcf(c_111672,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_111405]) ).

tcf(c_111673,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_111405]) ).

tcf(c_111674,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_111405]) ).

tcf(c_111675,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_111405]) ).

tcf(c_111676,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_111405]) ).

tcf(c_111677,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_111405]) ).

tcf(c_111678,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_111405]) ).

tcf(c_111679,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_111405]) ).

tcf(c_111680,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_111405]) ).

tcf(c_111681,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_111405]) ).

tcf(c_111682,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_111405]) ).

tcf(c_111683,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_111405]) ).

tcf(c_111684,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_111405]) ).

tcf(c_111685,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_111405]) ).

tcf(c_111686,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_111405]) ).

tcf(c_111687,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_111405]) ).

tcf(c_111688,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_111405]) ).

tcf(c_111689,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_111405]) ).

tcf(c_111690,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_111405]) ).

tcf(c_111691,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_111405]) ).

tcf(c_111692,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_111405]) ).

tcf(c_111693,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_111405]) ).

tcf(c_111694,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_111405]) ).

tcf(c_111695,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_111405]) ).

tcf(c_111696,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_111405]) ).

tcf(c_111697,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_111405]) ).

tcf(c_111698,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_111405]) ).

tcf(c_111699,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_111405]) ).

tcf(c_111700,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_111405]) ).

tcf(c_111701,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_111405]) ).

tcf(c_111702,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_111405]) ).

tcf(c_111703,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_111405]) ).

tcf(c_111704,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_111405]) ).

tcf(c_111705,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_111405]) ).

tcf(c_111706,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_111405]) ).

tcf(c_111707,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_111405]) ).

tcf(c_111708,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_111405]) ).

tcf(c_111709,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_111405]) ).

tcf(c_111710,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_111405]) ).

tcf(c_111711,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_111405]) ).

tcf(c_111712,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_111405]) ).

tcf(c_111713,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_111405]) ).

tcf(c_111714,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_111405]) ).

tcf(c_111715,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_111405]) ).

tcf(c_111716,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_111405]) ).

tcf(c_111717,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_111405]) ).

tcf(c_111718,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_111405]) ).

tcf(c_111719,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_111405]) ).

tcf(c_111720,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_111405]) ).

tcf(c_111723,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_92656]) ).

tcf(c_111724,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_111405,c_255]) ).

tcf(c_111726,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111405,c_256]) ).

tcf(c_111728,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111405,c_83532]) ).

tcf(c_111729,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111405,c_83524]) ).

tcf(c_111730,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_111405]) ).

tcf(c_111731,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_111079]) ).

tcf(c_111732,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_110591]) ).

tcf(c_111733,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_109784]) ).

tcf(c_111734,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_109567]) ).

tcf(c_111735,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_108992]) ).

tcf(c_111736,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_107183]) ).

tcf(c_111740,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_106960]) ).

tcf(c_111741,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_105967]) ).

tcf(c_111743,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_95608]) ).

tcf(c_111746,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111405,c_98014]) ).

tcf(c_111747,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_95414]) ).

tcf(c_111748,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_95286]) ).

tcf(c_111749,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_95041]) ).

tcf(c_111750,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_94695]) ).

tcf(c_111751,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_94594]) ).

tcf(c_111752,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_93822]) ).

tcf(c_111753,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_93551]) ).

tcf(c_111754,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111405,c_79918]) ).

tcf(c_111757,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111405,c_83537]) ).

tcf(c_111758,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111405,c_83534]) ).

tcf(c_111764,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111405,c_96186]) ).

tcf(c_111765,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111668,c_59636]) ).

tcf(c_111766,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111663,c_79190]) ).

tcf(c_111767,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111754,c_76415]) ).

tcf(c_111768,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111671,c_76855,c_93903]) ).

tcf(c_111772,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111746,c_79573]) ).

tcf(c_111904,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_92656]) ).

tcf(c_111905,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_111320,c_255]) ).

tcf(c_111907,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111320,c_256]) ).

tcf(c_111909,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111320,c_83532]) ).

tcf(c_111910,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111320,c_83524]) ).

tcf(c_111911,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_111405]) ).

tcf(c_111912,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_111079]) ).

tcf(c_111913,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_110591]) ).

tcf(c_111914,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_109784]) ).

tcf(c_111915,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_109567]) ).

tcf(c_111916,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_108992]) ).

tcf(c_111917,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_107183]) ).

tcf(c_111921,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_106960]) ).

tcf(c_111922,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_105967]) ).

tcf(c_111924,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_95608]) ).

tcf(c_111927,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111320,c_98014]) ).

tcf(c_111928,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_95414]) ).

tcf(c_111929,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_95286]) ).

tcf(c_111930,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_95041]) ).

tcf(c_111931,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_94695]) ).

tcf(c_111932,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_94594]) ).

tcf(c_111933,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_93822]) ).

tcf(c_111934,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_93551]) ).

tcf(c_111935,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111320,c_79918]) ).

tcf(c_111938,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111320,c_83537]) ).

tcf(c_111939,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111320,c_83534]) ).

tcf(c_111945,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111320,c_96186]) ).

tcf(c_111952,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_111927,c_79573]) ).

tcf(c_111982,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_111767]) ).

tcf(c_111983,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_111767]) ).

tcf(c_111984,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_111767]) ).

tcf(c_111985,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_111767]) ).

tcf(c_111987,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_111767]) ).

tcf(c_111988,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_111767]) ).

tcf(c_111990,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_111767]) ).

tcf(c_111991,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_111767]) ).

tcf(c_111992,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_111767]) ).

tcf(c_111993,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_111767]) ).

tcf(c_111994,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_111767]) ).

tcf(c_111995,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_111767]) ).

tcf(c_111996,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_111767]) ).

tcf(c_111997,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_111767]) ).

tcf(c_111998,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_111767]) ).

tcf(c_111999,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_111767]) ).

tcf(c_112000,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_111767]) ).

tcf(c_112001,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_111767]) ).

tcf(c_112002,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_111767]) ).

tcf(c_112003,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_111767]) ).

tcf(c_112004,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_111767]) ).

tcf(c_112005,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_111767]) ).

tcf(c_112006,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_111767]) ).

tcf(c_112007,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_111767]) ).

tcf(c_112008,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_111767]) ).

tcf(c_112009,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_111767]) ).

tcf(c_112010,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_111767]) ).

tcf(c_112011,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_111767]) ).

tcf(c_112012,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_111767]) ).

tcf(c_112013,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_111767]) ).

tcf(c_112014,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_111767]) ).

tcf(c_112015,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_111767]) ).

tcf(c_112016,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_111767]) ).

tcf(c_112017,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_111767]) ).

tcf(c_112018,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_111767]) ).

tcf(c_112019,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_111767]) ).

tcf(c_112020,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_111767]) ).

tcf(c_112021,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_111767]) ).

tcf(c_112022,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_111767]) ).

tcf(c_112023,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_111767]) ).

tcf(c_112024,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_111767]) ).

tcf(c_112025,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_111767]) ).

tcf(c_112026,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_111767]) ).

tcf(c_112027,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_111767]) ).

tcf(c_112028,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_111767]) ).

tcf(c_112029,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_111767]) ).

tcf(c_112030,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_111767]) ).

tcf(c_112031,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_111767]) ).

tcf(c_112032,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_111767]) ).

tcf(c_112033,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_111767]) ).

tcf(c_112034,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_111767]) ).

tcf(c_112035,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_111767]) ).

tcf(c_112036,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_111767]) ).

tcf(c_112037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_111767]) ).

tcf(c_112038,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_111767]) ).

tcf(c_112039,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_111767]) ).

tcf(c_112040,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_111767]) ).

tcf(c_112041,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_111767]) ).

tcf(c_112044,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_92656]) ).

tcf(c_112045,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_111767,c_255]) ).

tcf(c_112047,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111767,c_256]) ).

tcf(c_112049,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111767,c_83532]) ).

tcf(c_112050,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_111767,c_83524]) ).

tcf(c_112051,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_111767]) ).

tcf(c_112052,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_111405]) ).

tcf(c_112053,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_111079]) ).

tcf(c_112054,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_110591]) ).

tcf(c_112055,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_109784]) ).

tcf(c_112056,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_109567]) ).

tcf(c_112057,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_108992]) ).

tcf(c_112058,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_107183]) ).

tcf(c_112062,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_106960]) ).

tcf(c_112063,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_105967]) ).

tcf(c_112065,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_95608]) ).

tcf(c_112068,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111767,c_98014]) ).

tcf(c_112069,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_95414]) ).

tcf(c_112070,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_95286]) ).

tcf(c_112071,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_95041]) ).

tcf(c_112072,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_94695]) ).

tcf(c_112073,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_94594]) ).

tcf(c_112074,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_93822]) ).

tcf(c_112075,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_93551]) ).

tcf(c_112076,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111767,c_79918]) ).

tcf(c_112079,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111767,c_83537]) ).

tcf(c_112080,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111767,c_83534]) ).

tcf(c_112086,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111767,c_96186]) ).

tcf(c_112087,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111987,c_59636]) ).

tcf(c_112088,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111982,c_79190]) ).

tcf(c_112089,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_112076,c_76415]) ).

tcf(c_112090,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_111990,c_76855,c_93903]) ).

tcf(c_112094,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_112068,c_79573]) ).

tcf(c_112293,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_84340,c_90801,c_91937,c_91938,c_91975]) ).

tcf(c_112294,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_253,c_112293]) ).

tcf(c_112297,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_93551,c_112293]) ).

tcf(c_112330,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),pls))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),pls)),
    inference(superposition,[status(thm)],[c_574,c_112293]) ).

tcf(c_112331,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),min))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),min)),
    inference(superposition,[status(thm)],[c_76397,c_112293]) ).

tcf(c_112332,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),one_one_int))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_112293]) ).

tcf(c_112333,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),undefined_int(int)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_112293]) ).

tcf(c_112334,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_76399,c_112293]) ).

tcf(c_112335,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_76401,c_112293]) ).

tcf(c_112336,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),m))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),m)),
    inference(superposition,[status(thm)],[c_76402,c_112293]) ).

tcf(c_112337,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s1))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s1)),
    inference(superposition,[status(thm)],[c_76403,c_112293]) ).

tcf(c_112338,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),s)),
    inference(superposition,[status(thm)],[c_76404,c_112293]) ).

tcf(c_112339,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),t))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),t)),
    inference(superposition,[status(thm)],[c_76405,c_112293]) ).

tcf(c_112340,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK9))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_112293]) ).

tcf(c_112341,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK10))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_112293]) ).

tcf(c_112342,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK11))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_112293]) ).

tcf(c_112343,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK13))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_112293]) ).

tcf(c_112344,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_14))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_112293]) ).

tcf(c_112345,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_15))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_112293]) ).

tcf(c_112346,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_16))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_112293]) ).

tcf(c_112347,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_17))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_112293]) ).

tcf(c_112348,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_18))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_112293]) ).

tcf(c_112349,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_112293]) ).

tcf(c_112350,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_77366,c_112293]) ).

tcf(c_112351,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0))),
    inference(superposition,[status(thm)],[c_78024,c_112293]) ).

tcf(c_112352,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X0,t)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X0,t))),
    inference(superposition,[status(thm)],[c_78042,c_112293]) ).

tcf(c_112353,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_112293]) ).

tcf(c_112354,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_112293]) ).

tcf(c_112356,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_112293]) ).

tcf(c_112358,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_112293]) ).

tcf(c_112359,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_112293]) ).

tcf(c_112361,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_112293]) ).

tcf(c_112362,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_112293]) ).

tcf(c_112363,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_112293]) ).

tcf(c_112364,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_112293]) ).

tcf(c_112365,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_112293]) ).

tcf(c_112366,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_112293]) ).

tcf(c_112367,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_112293]) ).

tcf(c_112368,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96714,c_112293]) ).

tcf(c_112369,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_99171,c_112293]) ).

tcf(c_112370,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_112293]) ).

tcf(c_112371,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_112293]) ).

tcf(c_112373,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_112293,c_93890]) ).

tcf(c_112374,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_112293,c_1042]) ).

tcf(c_112375,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_112293,c_78295]) ).

tcf(c_112376,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)) ),
    inference(superposition,[status(thm)],[c_112293,c_1027]) ).

tcf(c_112378,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = pls,
    inference(superposition,[status(thm)],[c_112293,c_92002]) ).

tcf(c_112379,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),X1),
    inference(superposition,[status(thm)],[c_112293,c_252]) ).

tcf(c_112380,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_112293,c_833]) ).

tcf(c_112382,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_112293,c_76535]) ).

tcf(c_112383,plain,
    ! [X0: $i] : hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))),
    inference(superposition,[status(thm)],[c_112293,c_76498]) ).

tcf(c_112384,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),
    inference(superposition,[status(thm)],[c_112293,c_1045]) ).

tcf(c_112386,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_112293,c_1039]) ).

tcf(c_112387,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_112293,c_217]) ).

tcf(c_112389,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),
    inference(superposition,[status(thm)],[c_112293,c_833]) ).

tcf(c_112390,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_112293,c_108222]) ).

tcf(c_112393,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_13,iPr_def_14))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(iPr_def_13,iPr_def_14)),
    inference(light_normalisation,[status(thm)],[c_112336,c_79190]) ).

tcf(c_112394,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(light_normalisation,[status(thm)],[c_112373,c_59638]) ).

tcf(c_112454,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(div_mod_nat(X1),X0)),sK36(hAPP_nat_nat(div_mod_nat(X1),X0),X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1683,c_1583]) ).

tcf(c_112455,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(div_mod_nat(X1),X0)),X0) = hAPP_nat_nat(div_mod_nat(X1),X0) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1683,c_1693]) ).

tcf(c_112457,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)),
    inference(superposition,[status(thm)],[c_1683,c_1317]) ).

tcf(c_112459,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X2),hAPP_nat_nat(div_mod_nat(X0),X1))),X1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(div_mod_nat(X0),X1))) ),
    inference(superposition,[status(thm)],[c_1683,c_1712]) ).

tcf(c_112474,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(times_times_nat(X0),X1))),X1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1),
    inference(superposition,[status(thm)],[c_79342,c_1689]) ).

tcf(c_112475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X2)),X3))),X2) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(X0),X3)),X2),
    inference(superposition,[status(thm)],[c_1285,c_1689]) ).

tcf(c_112477,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X2) = hAPP_nat_nat(div_mod_nat(X0),X2),
    inference(superposition,[status(thm)],[c_1284,c_1689]) ).

tcf(c_112478,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(iPr_def_10,hAPP_nat_nat(times_times_nat(X0),X1))),X1) = hAPP_nat_nat(div_mod_nat(one_one_nat),X1),
    inference(superposition,[status(thm)],[c_77521,c_1689]) ).

tcf(c_112479,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),hAPP_nat_nat(times_times_nat(X1),X2))),X2) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X2),
    inference(superposition,[status(thm)],[c_94015,c_1689]) ).

tcf(c_112480,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1) = hAPP_nat_nat(div_mod_nat(zero_zero_nat),X1),
    inference(superposition,[status(thm)],[c_1325,c_1689]) ).

tcf(c_112481,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),X1)),X0) = hAPP_nat_nat(div_mod_nat(X1),X0),
    inference(superposition,[status(thm)],[c_82316,c_1689]) ).

tcf(c_112483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)),X2) = hAPP_nat_nat(div_mod_nat(X3),X2),
    inference(superposition,[status(thm)],[c_1308,c_1689]) ).

tcf(c_112484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),X3)),hAPP_nat_nat(times_times_nat(X0),X2)) = hAPP_nat_nat(div_mod_nat(X3),hAPP_nat_nat(times_times_nat(X0),X2)),
    inference(superposition,[status(thm)],[c_218,c_1689]) ).

tcf(c_112486,plain,
    ! [X0: $i,X1: $i,X2: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2)),X0) = hAPP_nat_nat(div_mod_nat(X2),X0),
    inference(superposition,[status(thm)],[c_1309,c_1689]) ).

tcf(c_112487,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),one_one_nat) = hAPP_nat_nat(div_mod_nat(X1),one_one_nat),
    inference(superposition,[status(thm)],[c_1413,c_1689]) ).

tcf(c_112488,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(X0),X1)),X0) = hAPP_nat_nat(div_mod_nat(X1),X0),
    inference(superposition,[status(thm)],[c_1417,c_1689]) ).

tcf(c_112489,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0)),X1) = hAPP_nat_nat(div_mod_nat(X0),X1),
    inference(superposition,[status(thm)],[c_1336,c_1689]) ).

tcf(c_112490,plain,
    ! [X0: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0)),zero_zero_nat) = hAPP_nat_nat(div_mod_nat(X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1337,c_1689]) ).

tcf(c_112492,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X1)),X0))),
    inference(superposition,[status(thm)],[c_1689,c_1694]) ).

tcf(c_112495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(div_mod_nat(X2),X1)))
      | ~ sP4(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2),X3,X1) ),
    inference(superposition,[status(thm)],[c_1689,c_1711]) ).

tcf(c_112496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X3),X2)),X1),X0,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2))) ),
    inference(superposition,[status(thm)],[c_1689,c_1712]) ).

tcf(c_112505,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(iPr_def_11),hAPP_nat_nat(times_times_nat(X0),X1))),X1) = zero_zero_nat,
    inference(light_normalisation,[status(thm)],[c_112474,c_77667]) ).

tcf(c_112566,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79150,c_12163]) ).

tcf(c_112569,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_93890,c_12163]) ).

tcf(c_112570,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),hAPP_int_int(times_times_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_82861,c_12163]) ).

tcf(c_112571,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X1)))),hAPP_int_int(times_times_int(X2),X2)))),
    inference(superposition,[status(thm)],[c_252,c_12163]) ).

tcf(c_112572,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X1))),hAPP_int_int(times_times_int(X2),X2)))),
    inference(superposition,[status(thm)],[c_217,c_12163]) ).

tcf(c_112575,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(times_times_int(X0),X0))),hAPP_int_int(times_times_int(X1),X1)))),
    inference(superposition,[status(thm)],[c_382,c_12163]) ).

tcf(c_112576,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_1001,c_12163]) ).

tcf(c_112577,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79464,c_12163]) ).

tcf(c_112579,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_79150,c_12163]) ).

tcf(c_112580,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),hAPP_int_int(times_times_int(X0),X0)))),
    inference(superposition,[status(thm)],[c_59637,c_12163]) ).

tcf(c_112581,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_nat_int(power_power_int(X1),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_82861,c_12163]) ).

tcf(c_112582,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X2),hAPP_int_int(times_times_int(X1),X2)))))),
    inference(superposition,[status(thm)],[c_252,c_12163]) ).

tcf(c_112583,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),X2)),X2))))),
    inference(superposition,[status(thm)],[c_217,c_12163]) ).

tcf(c_112586,plain,
    ! [X0: $i,X1: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),number_number_of_int(hAPP_int_int(times_times_int(X1),X1))))),
    inference(superposition,[status(thm)],[c_382,c_12163]) ).

tcf(c_112587,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),pls))),
    inference(superposition,[status(thm)],[c_1001,c_12163]) ).

tcf(c_112588,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),one_one_int))),
    inference(superposition,[status(thm)],[c_79464,c_12163]) ).

tcf(c_112590,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(plus_plus_int(iPr_def_14),iPr_def_14)))),
    inference(superposition,[status(thm)],[c_79150,c_12163]) ).

tcf(c_112591,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(iPr_def_13,m)))),
    inference(superposition,[status(thm)],[c_59637,c_12163]) ).

tcf(c_112593,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),X0)))),
    inference(light_normalisation,[status(thm)],[c_112577,c_59636]) ).

tcf(c_112596,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X0),X1)),iPr_def_11)),hAPP_int_int(times_times_int(X2),X2)))),
    inference(light_normalisation,[status(thm)],[c_112572,c_90904]) ).

tcf(c_112644,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(s1,hAPP_int_int(times_times_int(s1),X0)),s1)),
    inference(superposition,[status(thm)],[c_253,c_78305]) ).

tcf(c_112646,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(s1,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),s1))),s1)),
    inference(superposition,[status(thm)],[c_252,c_78305]) ).

tcf(c_112647,plain,
    hBOOL(hAPP_int_bool(zcong(s1,pls),s1)),
    inference(superposition,[status(thm)],[c_1004,c_78305]) ).

tcf(c_112648,plain,
    hBOOL(hAPP_int_bool(zcong(s1,hAPP_int_int(plus_plus_int(s1),s1)),s1)),
    inference(superposition,[status(thm)],[c_79150,c_78305]) ).

tcf(c_112649,plain,
    hBOOL(hAPP_int_bool(zcong(s1,hAPP_int_int(iPr_def_13,s1)),s1)),
    inference(superposition,[status(thm)],[c_59637,c_78305]) ).

tcf(c_112650,plain,
    ! [X0: $i] : hBOOL(member_int(s1,zcong(s1,hAPP_int_int(times_times_int(X0),s1)))),
    inference(superposition,[status(thm)],[c_78305,c_226]) ).

tcf(c_112651,plain,
    ! [X0: $i] :
      ( is_int(sK14(s1,hAPP_int_int(times_times_int(X0),s1),s1))
      | ~ is_int(hAPP_int_int(times_times_int(X0),s1)) ),
    inference(superposition,[status(thm)],[c_78305,c_852]) ).

tcf(c_112659,plain,
    hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_112349,c_253]) ).

tcf(c_112661,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,one_one_int)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_112659,c_93890]) ).

tcf(c_112662,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_112659,c_1042]) ).

tcf(c_112663,plain,
    hBOOL(hAPP_int_bool(zcong(pls,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_112659,c_78295]) ).

tcf(c_112666,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),sK30(iPr_def_19)))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = pls,
    inference(superposition,[status(thm)],[c_112659,c_92002]) ).

tcf(c_112667,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0),
    inference(superposition,[status(thm)],[c_112659,c_252]) ).

tcf(c_112668,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_112659,c_833]) ).

tcf(c_112670,plain,
    hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int))),
    inference(superposition,[status(thm)],[c_112659,c_76535]) ).

tcf(c_112671,plain,
    hBOOL(member_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),
    inference(superposition,[status(thm)],[c_112659,c_76498]) ).

tcf(c_112672,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_112659,c_1045]) ).

tcf(c_112674,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
    inference(superposition,[status(thm)],[c_112659,c_1039]) ).

tcf(c_112675,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_112659,c_217]) ).

tcf(c_112677,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),
    inference(superposition,[status(thm)],[c_112659,c_833]) ).

tcf(c_112678,plain,
    is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))),
    inference(superposition,[status(thm)],[c_112659,c_98875]) ).

tcf(c_112679,plain,
    hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_int) = pls,
    inference(superposition,[status(thm)],[c_112659,c_108794]) ).

tcf(c_112682,plain,
    hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(light_normalisation,[status(thm)],[c_112661,c_59638]) ).

tcf(c_112745,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_92656]) ).

tcf(c_112746,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_111679,c_255]) ).

tcf(c_112748,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111679,c_256]) ).

tcf(c_112751,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111679,c_83532]) ).

tcf(c_112752,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111679,c_83524]) ).

tcf(c_112753,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_111767]) ).

tcf(c_112754,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_111405]) ).

tcf(c_112755,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_111079]) ).

tcf(c_112756,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_110591]) ).

tcf(c_112757,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_109784]) ).

tcf(c_112758,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_109567]) ).

tcf(c_112759,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_108992]) ).

tcf(c_112760,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_107183]) ).

tcf(c_112764,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_106960]) ).

tcf(c_112765,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_105967]) ).

tcf(c_112767,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_95608]) ).

tcf(c_112770,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111679,c_98014]) ).

tcf(c_112771,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_95414]) ).

tcf(c_112772,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_95286]) ).

tcf(c_112773,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_95041]) ).

tcf(c_112774,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_94695]) ).

tcf(c_112775,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_94594]) ).

tcf(c_112776,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_93822]) ).

tcf(c_112777,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_93551]) ).

tcf(c_112778,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111679,c_79918]) ).

tcf(c_112781,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111679,c_83537]) ).

tcf(c_112782,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111679,c_83534]) ).

tcf(c_112788,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111679,c_96186]) ).

tcf(c_112795,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_112770,c_79573]) ).

tcf(c_112856,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_112089]) ).

tcf(c_112857,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_112089]) ).

tcf(c_112858,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_112089]) ).

tcf(c_112859,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_112089]) ).

tcf(c_112861,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_112089]) ).

tcf(c_112862,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_112089]) ).

tcf(c_112864,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_112089]) ).

tcf(c_112865,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_112089]) ).

tcf(c_112866,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_112089]) ).

tcf(c_112867,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_112089]) ).

tcf(c_112868,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_112089]) ).

tcf(c_112869,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_112089]) ).

tcf(c_112870,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_112089]) ).

tcf(c_112871,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_112089]) ).

tcf(c_112872,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_112089]) ).

tcf(c_112873,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_112089]) ).

tcf(c_112874,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_112089]) ).

tcf(c_112875,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_112089]) ).

tcf(c_112876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_112089]) ).

tcf(c_112877,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_112089]) ).

tcf(c_112878,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_112089]) ).

tcf(c_112879,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_112089]) ).

tcf(c_112880,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_112089]) ).

tcf(c_112881,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_112089]) ).

tcf(c_112882,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_112089]) ).

tcf(c_112883,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_112089]) ).

tcf(c_112884,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_112089]) ).

tcf(c_112885,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_112089]) ).

tcf(c_112886,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_112089]) ).

tcf(c_112887,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_112089]) ).

tcf(c_112888,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_112089]) ).

tcf(c_112889,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_112089]) ).

tcf(c_112890,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_112089]) ).

tcf(c_112891,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_112089]) ).

tcf(c_112892,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_112089]) ).

tcf(c_112893,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_112089]) ).

tcf(c_112894,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_112089]) ).

tcf(c_112895,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_112089]) ).

tcf(c_112896,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_112089]) ).

tcf(c_112897,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_112089]) ).

tcf(c_112898,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_112089]) ).

tcf(c_112899,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_112089]) ).

tcf(c_112900,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_112089]) ).

tcf(c_112901,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_112089]) ).

tcf(c_112902,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_112089]) ).

tcf(c_112903,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_112089]) ).

tcf(c_112904,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_112089]) ).

tcf(c_112905,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_112089]) ).

tcf(c_112906,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_112089]) ).

tcf(c_112907,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_112089]) ).

tcf(c_112908,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_112089]) ).

tcf(c_112909,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_112089]) ).

tcf(c_112910,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_112089]) ).

tcf(c_112911,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_112089]) ).

tcf(c_112912,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_112089]) ).

tcf(c_112913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_112089]) ).

tcf(c_112914,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_112089]) ).

tcf(c_112915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_112089]) ).

tcf(c_112916,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_112089]) ).

tcf(c_112917,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_112089]) ).

tcf(c_112920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_92656]) ).

tcf(c_112921,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_112089,c_255]) ).

tcf(c_112923,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112089,c_256]) ).

tcf(c_112926,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_112089,c_83532]) ).

tcf(c_112927,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_112089,c_83524]) ).

tcf(c_112928,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_112089]) ).

tcf(c_112929,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_111767]) ).

tcf(c_112930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_111405]) ).

tcf(c_112931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_111079]) ).

tcf(c_112932,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_110591]) ).

tcf(c_112933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_109784]) ).

tcf(c_112934,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_109567]) ).

tcf(c_112935,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_108992]) ).

tcf(c_112936,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_107183]) ).

tcf(c_112940,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_106960]) ).

tcf(c_112941,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_105967]) ).

tcf(c_112943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_95608]) ).

tcf(c_112946,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_112089,c_98014]) ).

tcf(c_112947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_95414]) ).

tcf(c_112948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_95286]) ).

tcf(c_112949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_95041]) ).

tcf(c_112950,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_94695]) ).

tcf(c_112951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_94594]) ).

tcf(c_112952,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_93822]) ).

tcf(c_112953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_93551]) ).

tcf(c_112954,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112089,c_79918]) ).

tcf(c_112957,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112089,c_83537]) ).

tcf(c_112958,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112089,c_83534]) ).

tcf(c_112964,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112089,c_96186]) ).

tcf(c_112965,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_112861,c_59636]) ).

tcf(c_112966,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_112856,c_79190]) ).

tcf(c_112967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_112954,c_76415]) ).

tcf(c_112968,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_112864,c_76855,c_93903]) ).

tcf(c_112972,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_112946,c_79573]) ).

tcf(c_113200,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_92656]) ).

tcf(c_113201,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_111998,c_255]) ).

tcf(c_113203,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111998,c_256]) ).

tcf(c_113206,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111998,c_83532]) ).

tcf(c_113207,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_111998,c_83524]) ).

tcf(c_113208,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_112089]) ).

tcf(c_113209,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_111767]) ).

tcf(c_113210,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_111405]) ).

tcf(c_113211,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_111079]) ).

tcf(c_113212,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_110591]) ).

tcf(c_113213,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_109784]) ).

tcf(c_113214,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_109567]) ).

tcf(c_113215,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_108992]) ).

tcf(c_113216,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_107183]) ).

tcf(c_113220,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_106960]) ).

tcf(c_113221,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_105967]) ).

tcf(c_113223,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_95608]) ).

tcf(c_113226,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_111998,c_98014]) ).

tcf(c_113227,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_95414]) ).

tcf(c_113228,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_95286]) ).

tcf(c_113229,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_95041]) ).

tcf(c_113230,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_94695]) ).

tcf(c_113231,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_94594]) ).

tcf(c_113232,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_93822]) ).

tcf(c_113233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_93551]) ).

tcf(c_113234,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111998,c_79918]) ).

tcf(c_113237,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111998,c_83537]) ).

tcf(c_113238,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111998,c_83534]) ).

tcf(c_113244,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_111998,c_96186]) ).

tcf(c_113251,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_113226,c_79573]) ).

tcf(c_113305,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_112967]) ).

tcf(c_113306,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_112967]) ).

tcf(c_113307,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_112967]) ).

tcf(c_113308,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_112967]) ).

tcf(c_113310,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_112967]) ).

tcf(c_113311,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_112967]) ).

tcf(c_113313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_112967]) ).

tcf(c_113314,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_112967]) ).

tcf(c_113315,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_112967]) ).

tcf(c_113316,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_112967]) ).

tcf(c_113317,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_112967]) ).

tcf(c_113318,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_112967]) ).

tcf(c_113319,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_112967]) ).

tcf(c_113320,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_112967]) ).

tcf(c_113321,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_112967]) ).

tcf(c_113322,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_112967]) ).

tcf(c_113323,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_112967]) ).

tcf(c_113324,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_112967]) ).

tcf(c_113325,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_112967]) ).

tcf(c_113326,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_112967]) ).

tcf(c_113327,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_112967]) ).

tcf(c_113328,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_112967]) ).

tcf(c_113329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_112967]) ).

tcf(c_113330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_112967]) ).

tcf(c_113331,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_112967]) ).

tcf(c_113332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_112967]) ).

tcf(c_113333,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_112967]) ).

tcf(c_113334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_112967]) ).

tcf(c_113335,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_112967]) ).

tcf(c_113336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_112967]) ).

tcf(c_113337,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_112967]) ).

tcf(c_113338,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_112967]) ).

tcf(c_113339,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_112967]) ).

tcf(c_113340,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_112967]) ).

tcf(c_113341,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_112967]) ).

tcf(c_113342,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_112967]) ).

tcf(c_113343,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_112967]) ).

tcf(c_113344,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_112967]) ).

tcf(c_113345,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_112967]) ).

tcf(c_113346,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_112967]) ).

tcf(c_113347,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_112967]) ).

tcf(c_113348,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_112967]) ).

tcf(c_113349,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_112967]) ).

tcf(c_113350,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_112967]) ).

tcf(c_113351,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_112967]) ).

tcf(c_113352,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_112967]) ).

tcf(c_113353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_112967]) ).

tcf(c_113354,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_112967]) ).

tcf(c_113355,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_112967]) ).

tcf(c_113356,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_112967]) ).

tcf(c_113357,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_112967]) ).

tcf(c_113358,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_112967]) ).

tcf(c_113359,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_112967]) ).

tcf(c_113360,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_112967]) ).

tcf(c_113361,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_112967]) ).

tcf(c_113362,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_112967]) ).

tcf(c_113363,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_112967]) ).

tcf(c_113364,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_112967]) ).

tcf(c_113365,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_112967]) ).

tcf(c_113366,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_112967]) ).

tcf(c_113367,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_112967]) ).

tcf(c_113368,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_112967]) ).

tcf(c_113371,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_92656]) ).

tcf(c_113372,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_112967,c_255]) ).

tcf(c_113374,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112967,c_256]) ).

tcf(c_113377,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_112967,c_83532]) ).

tcf(c_113378,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_112967,c_83524]) ).

tcf(c_113379,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_112967]) ).

tcf(c_113380,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_112089]) ).

tcf(c_113381,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_111767]) ).

tcf(c_113382,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_111405]) ).

tcf(c_113383,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_111079]) ).

tcf(c_113384,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_110591]) ).

tcf(c_113385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_109784]) ).

tcf(c_113386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_109567]) ).

tcf(c_113387,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_108992]) ).

tcf(c_113388,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_107183]) ).

tcf(c_113392,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_106960]) ).

tcf(c_113393,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_105967]) ).

tcf(c_113395,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_95608]) ).

tcf(c_113398,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_112967,c_98014]) ).

tcf(c_113399,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_95414]) ).

tcf(c_113400,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_95286]) ).

tcf(c_113401,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_95041]) ).

tcf(c_113402,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_94695]) ).

tcf(c_113403,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_94594]) ).

tcf(c_113404,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_93822]) ).

tcf(c_113405,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_93551]) ).

tcf(c_113406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112967,c_79918]) ).

tcf(c_113409,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112967,c_83537]) ).

tcf(c_113410,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112967,c_83534]) ).

tcf(c_113416,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112967,c_96186]) ).

tcf(c_113417,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113310,c_59636]) ).

tcf(c_113418,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113305,c_79190]) ).

tcf(c_113419,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113406,c_76415]) ).

tcf(c_113420,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113313,c_76855,c_93903]) ).

tcf(c_113424,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_113398,c_79573]) ).

tcf(c_113548,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_92656]) ).

tcf(c_113549,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_112872,c_255]) ).

tcf(c_113551,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112872,c_256]) ).

tcf(c_113554,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_112872,c_83532]) ).

tcf(c_113555,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_112872,c_83524]) ).

tcf(c_113556,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_112967]) ).

tcf(c_113557,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_112089]) ).

tcf(c_113558,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_111767]) ).

tcf(c_113559,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_111405]) ).

tcf(c_113560,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_111079]) ).

tcf(c_113561,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_110591]) ).

tcf(c_113562,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_109784]) ).

tcf(c_113563,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_109567]) ).

tcf(c_113564,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_108992]) ).

tcf(c_113565,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_107183]) ).

tcf(c_113569,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_106960]) ).

tcf(c_113570,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_105967]) ).

tcf(c_113572,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_95608]) ).

tcf(c_113575,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_112872,c_98014]) ).

tcf(c_113576,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_95414]) ).

tcf(c_113577,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_95286]) ).

tcf(c_113578,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_95041]) ).

tcf(c_113579,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_94695]) ).

tcf(c_113580,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_94594]) ).

tcf(c_113581,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_93822]) ).

tcf(c_113582,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_93551]) ).

tcf(c_113583,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112872,c_79918]) ).

tcf(c_113586,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112872,c_83537]) ).

tcf(c_113587,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112872,c_83534]) ).

tcf(c_113593,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_112872,c_96186]) ).

tcf(c_113600,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_113575,c_79573]) ).

tcf(c_113627,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_113419]) ).

tcf(c_113628,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_113419]) ).

tcf(c_113629,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_113419]) ).

tcf(c_113630,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_113419]) ).

tcf(c_113632,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_113419]) ).

tcf(c_113633,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_113419]) ).

tcf(c_113635,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_113419]) ).

tcf(c_113636,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_113419]) ).

tcf(c_113637,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_113419]) ).

tcf(c_113638,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_113419]) ).

tcf(c_113639,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_113419]) ).

tcf(c_113640,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_113419]) ).

tcf(c_113641,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_113419]) ).

tcf(c_113642,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_113419]) ).

tcf(c_113643,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_113419]) ).

tcf(c_113644,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_113419]) ).

tcf(c_113645,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_113419]) ).

tcf(c_113646,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_113419]) ).

tcf(c_113647,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_113419]) ).

tcf(c_113648,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_113419]) ).

tcf(c_113649,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_113419]) ).

tcf(c_113650,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_113419]) ).

tcf(c_113651,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_113419]) ).

tcf(c_113652,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_113419]) ).

tcf(c_113653,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_113419]) ).

tcf(c_113654,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_113419]) ).

tcf(c_113655,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_113419]) ).

tcf(c_113656,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_113419]) ).

tcf(c_113657,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_113419]) ).

tcf(c_113658,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_113419]) ).

tcf(c_113659,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_113419]) ).

tcf(c_113660,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_113419]) ).

tcf(c_113661,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_113419]) ).

tcf(c_113662,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_113419]) ).

tcf(c_113663,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_113419]) ).

tcf(c_113664,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_113419]) ).

tcf(c_113665,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_113419]) ).

tcf(c_113666,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_113419]) ).

tcf(c_113667,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_113419]) ).

tcf(c_113668,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_113419]) ).

tcf(c_113669,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_113419]) ).

tcf(c_113670,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_113419]) ).

tcf(c_113671,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_113419]) ).

tcf(c_113672,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_113419]) ).

tcf(c_113673,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_113419]) ).

tcf(c_113674,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_113419]) ).

tcf(c_113675,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_113419]) ).

tcf(c_113676,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_113419]) ).

tcf(c_113677,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_113419]) ).

tcf(c_113678,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_113419]) ).

tcf(c_113679,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_113419]) ).

tcf(c_113680,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_113419]) ).

tcf(c_113681,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_113419]) ).

tcf(c_113682,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_113419]) ).

tcf(c_113683,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_113419]) ).

tcf(c_113684,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_113419]) ).

tcf(c_113685,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_113419]) ).

tcf(c_113686,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_113419]) ).

tcf(c_113687,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_113419]) ).

tcf(c_113688,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_113419]) ).

tcf(c_113689,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_113419]) ).

tcf(c_113690,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_113419]) ).

tcf(c_113691,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_113419]) ).

tcf(c_113692,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_113419]) ).

tcf(c_113695,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_92656]) ).

tcf(c_113696,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_113419,c_255]) ).

tcf(c_113698,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113419,c_256]) ).

tcf(c_113701,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_113419,c_83532]) ).

tcf(c_113702,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_113419,c_83524]) ).

tcf(c_113703,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_113419]) ).

tcf(c_113704,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_112967]) ).

tcf(c_113705,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_112089]) ).

tcf(c_113706,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_111767]) ).

tcf(c_113707,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_111405]) ).

tcf(c_113708,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_111079]) ).

tcf(c_113709,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_110591]) ).

tcf(c_113710,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_109784]) ).

tcf(c_113711,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_109567]) ).

tcf(c_113712,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_108992]) ).

tcf(c_113713,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_107183]) ).

tcf(c_113717,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_106960]) ).

tcf(c_113718,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_105967]) ).

tcf(c_113720,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_95608]) ).

tcf(c_113723,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_113419,c_98014]) ).

tcf(c_113724,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_95414]) ).

tcf(c_113725,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_95286]) ).

tcf(c_113726,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_95041]) ).

tcf(c_113727,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_94695]) ).

tcf(c_113728,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_94594]) ).

tcf(c_113729,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_93822]) ).

tcf(c_113730,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_93551]) ).

tcf(c_113731,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113419,c_79918]) ).

tcf(c_113734,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113419,c_83537]) ).

tcf(c_113735,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113419,c_83534]) ).

tcf(c_113741,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113419,c_96186]) ).

tcf(c_113742,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113632,c_59636]) ).

tcf(c_113743,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113627,c_79190]) ).

tcf(c_113744,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113731,c_76415]) ).

tcf(c_113745,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_113635,c_76855,c_93903]) ).

tcf(c_113749,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_113723,c_79573]) ).

tcf(c_113945,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_92656]) ).

tcf(c_113946,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_113321,c_255]) ).

tcf(c_113948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113321,c_256]) ).

tcf(c_113951,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_113321,c_83532]) ).

tcf(c_113952,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_113321,c_83524]) ).

tcf(c_113953,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_113419]) ).

tcf(c_113954,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_112967]) ).

tcf(c_113955,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_112089]) ).

tcf(c_113956,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_111767]) ).

tcf(c_113957,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_111405]) ).

tcf(c_113958,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_111079]) ).

tcf(c_113959,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_110591]) ).

tcf(c_113960,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_109784]) ).

tcf(c_113961,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_109567]) ).

tcf(c_113962,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_108992]) ).

tcf(c_113963,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_107183]) ).

tcf(c_113967,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_106960]) ).

tcf(c_113968,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_105967]) ).

tcf(c_113970,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_95608]) ).

tcf(c_113973,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_113321,c_98014]) ).

tcf(c_113974,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_95414]) ).

tcf(c_113975,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_95286]) ).

tcf(c_113976,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_95041]) ).

tcf(c_113977,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_94695]) ).

tcf(c_113978,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_94594]) ).

tcf(c_113979,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_93822]) ).

tcf(c_113980,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_93551]) ).

tcf(c_113981,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113321,c_79918]) ).

tcf(c_113984,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113321,c_83537]) ).

tcf(c_113985,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113321,c_83534]) ).

tcf(c_113991,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113321,c_96186]) ).

tcf(c_113998,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_113973,c_79573]) ).

tcf(c_114019,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_79150,c_45878]) ).

tcf(c_114021,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_255,c_45878]) ).

tcf(c_114022,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_256,c_45878]) ).

tcf(c_114025,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_388,c_45878]) ).

tcf(c_114026,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_79190,c_45878]) ).

tcf(c_114027,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(superposition,[status(thm)],[c_59636,c_45878]) ).

tcf(c_114028,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X0)),pls)) ),
    inference(superposition,[status(thm)],[c_45878,c_46112]) ).

tcf(c_114029,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),d22set(pls))) ),
    inference(superposition,[status(thm)],[c_45878,c_1579]) ).

tcf(c_114030,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),hAPP_i1948725293t_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45878,c_226]) ).

tcf(c_114031,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45878,c_611]) ).

tcf(c_114032,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(light_normalisation,[status(thm)],[c_114027,c_59638]) ).

tcf(c_114045,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X0))) ),
    inference(light_normalisation,[status(thm)],[c_114025,c_79988]) ).

tcf(c_114048,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(plus_plus_int(X0),X1))) ),
    inference(light_normalisation,[status(thm)],[c_114022,c_92971]) ).

tcf(c_114108,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(minus_minus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_879,c_45986]) ).

tcf(c_114109,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
    inference(superposition,[status(thm)],[c_77403,c_45986]) ).

tcf(c_114110,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),min))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
    inference(superposition,[status(thm)],[c_78632,c_45986]) ).

tcf(c_114130,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(minus_minus_int(min),hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))) ),
    inference(superposition,[status(thm)],[c_78625,c_45986]) ).

tcf(c_114131,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),number_number_of_int(X1))) ),
    inference(superposition,[status(thm)],[c_83524,c_45986]) ).

tcf(c_114132,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))) ),
    inference(superposition,[status(thm)],[c_83534,c_45986]) ).

tcf(c_114133,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(s),s)),min)) ),
    inference(superposition,[status(thm)],[c_85161,c_45986]) ).

tcf(c_114137,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),pls)) ),
    inference(superposition,[status(thm)],[c_98913,c_45986]) ).

tcf(c_114138,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),pls)) ),
    inference(superposition,[status(thm)],[c_99039,c_45986]) ).

tcf(c_114139,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(minus_minus_int(X0),X1),cOMBC_int_int_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(superposition,[status(thm)],[c_45986,c_226]) ).

tcf(c_114167,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_79150,c_45990]) ).

tcf(c_114169,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(superposition,[status(thm)],[c_255,c_45990]) ).

tcf(c_114170,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(superposition,[status(thm)],[c_256,c_45990]) ).

tcf(c_114173,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),min)) ),
    inference(superposition,[status(thm)],[c_388,c_45990]) ).

tcf(c_114174,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,m),min)) ),
    inference(superposition,[status(thm)],[c_79190,c_45990]) ).

tcf(c_114176,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),cOMBC_int_int_bool(ord_less_int,min)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_45990,c_226]) ).

tcf(c_114183,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),min)) ),
    inference(light_normalisation,[status(thm)],[c_114173,c_79988]) ).

tcf(c_114186,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(light_normalisation,[status(thm)],[c_114170,c_92971]) ).

tcf(c_114196,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_79150,c_45994]) ).

tcf(c_114198,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(superposition,[status(thm)],[c_255,c_45994]) ).

tcf(c_114199,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(superposition,[status(thm)],[c_256,c_45994]) ).

tcf(c_114202,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),min)) ),
    inference(superposition,[status(thm)],[c_388,c_45994]) ).

tcf(c_114203,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,m),min)) ),
    inference(superposition,[status(thm)],[c_79190,c_45994]) ).

tcf(c_114205,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),cOMBC_int_int_bool(ord_less_eq_int,min)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),min)) ),
    inference(superposition,[status(thm)],[c_45994,c_226]) ).

tcf(c_114212,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),min)) ),
    inference(light_normalisation,[status(thm)],[c_114202,c_79988]) ).

tcf(c_114215,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,min),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),min)) ),
    inference(light_normalisation,[status(thm)],[c_114199,c_92971]) ).

tcf(c_114221,plain,
    hBOOL(member_int(s1,zcong(s1,hAPP_int_int(iPr_def_13,s1)))),
    inference(superposition,[status(thm)],[c_112649,c_226]) ).

tcf(c_114222,plain,
    ( is_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1))
    | ~ is_int(hAPP_int_int(iPr_def_13,s1)) ),
    inference(superposition,[status(thm)],[c_112649,c_852]) ).

tcf(c_114223,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,s1),s1),s1)),
    inference(superposition,[status(thm)],[c_112649,c_814]) ).

tcf(c_114224,plain,
    is_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_114222,c_77054]) ).

tcf(c_114233,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),X0)) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_46106]) ).

tcf(c_114234,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(s1,hAPP_int_int(iPr_def_13,s1),s1))),X0) = pls,
    inference(superposition,[status(thm)],[c_114224,c_46104]) ).

tcf(c_114235,plain,
    hAPP_int_int(minus_minus_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),pls) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_880]) ).

tcf(c_114236,plain,
    hAPP_nat_int(power_power_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),one_one_nat) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_608]) ).

tcf(c_114237,plain,
    hAPP_int_int(plus_plus_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),pls) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_524]) ).

tcf(c_114238,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_523]) ).

tcf(c_114239,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_347]) ).

tcf(c_114240,plain,
    hAPP_int_int(times_times_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)),one_one_int) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_346]) ).

tcf(c_114241,plain,
    number_number_of_int(sK14(s1,hAPP_int_int(iPr_def_13,s1),s1)) = sK14(s1,hAPP_int_int(iPr_def_13,s1),s1),
    inference(superposition,[status(thm)],[c_114224,c_254]) ).

tcf(c_114245,plain,
    hBOOL(member_int(s1,zcong(hAPP_int_int(iPr_def_13,s1),s1))),
    inference(superposition,[status(thm)],[c_114223,c_226]) ).

tcf(c_114246,plain,
    ( is_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1))
    | ~ is_int(s1) ),
    inference(superposition,[status(thm)],[c_114223,c_852]) ).

tcf(c_114248,plain,
    is_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_114246,c_71]) ).

tcf(c_114249,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_113744]) ).

tcf(c_114250,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_113744]) ).

tcf(c_114251,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_113744]) ).

tcf(c_114252,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_113744]) ).

tcf(c_114254,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_113744]) ).

tcf(c_114255,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_113744]) ).

tcf(c_114257,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_113744]) ).

tcf(c_114258,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_113744]) ).

tcf(c_114259,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_113744]) ).

tcf(c_114260,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_113744]) ).

tcf(c_114261,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_113744]) ).

tcf(c_114262,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_113744]) ).

tcf(c_114263,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_113744]) ).

tcf(c_114264,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_113744]) ).

tcf(c_114265,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_113744]) ).

tcf(c_114266,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_113744]) ).

tcf(c_114267,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_113744]) ).

tcf(c_114268,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_113744]) ).

tcf(c_114269,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_113744]) ).

tcf(c_114270,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_113744]) ).

tcf(c_114271,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_113744]) ).

tcf(c_114272,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_113744]) ).

tcf(c_114273,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_113744]) ).

tcf(c_114274,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_113744]) ).

tcf(c_114275,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_113744]) ).

tcf(c_114276,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_113744]) ).

tcf(c_114277,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_113744]) ).

tcf(c_114278,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_113744]) ).

tcf(c_114279,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_113744]) ).

tcf(c_114280,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_113744]) ).

tcf(c_114281,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_113744]) ).

tcf(c_114282,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_113744]) ).

tcf(c_114283,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_113744]) ).

tcf(c_114284,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_113744]) ).

tcf(c_114285,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_113744]) ).

tcf(c_114286,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_113744]) ).

tcf(c_114287,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_113744]) ).

tcf(c_114288,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_113744]) ).

tcf(c_114289,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_113744]) ).

tcf(c_114290,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_113744]) ).

tcf(c_114291,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_113744]) ).

tcf(c_114292,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_113744]) ).

tcf(c_114293,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_113744]) ).

tcf(c_114294,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_113744]) ).

tcf(c_114295,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_113744]) ).

tcf(c_114296,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_113744]) ).

tcf(c_114297,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_113744]) ).

tcf(c_114298,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_113744]) ).

tcf(c_114299,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_113744]) ).

tcf(c_114300,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_113744]) ).

tcf(c_114301,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_113744]) ).

tcf(c_114302,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_113744]) ).

tcf(c_114303,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_113744]) ).

tcf(c_114304,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_113744]) ).

tcf(c_114305,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_113744]) ).

tcf(c_114306,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_113744]) ).

tcf(c_114307,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_113744]) ).

tcf(c_114308,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_113744]) ).

tcf(c_114309,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_113744]) ).

tcf(c_114310,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_113744]) ).

tcf(c_114311,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_113744]) ).

tcf(c_114312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_113744]) ).

tcf(c_114313,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_113744]) ).

tcf(c_114314,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_113744]) ).

tcf(c_114315,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_113744]) ).

tcf(c_114316,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_113744]) ).

tcf(c_114319,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_92656]) ).

tcf(c_114320,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_113744,c_255]) ).

tcf(c_114322,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113744,c_256]) ).

tcf(c_114325,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_113744,c_83532]) ).

tcf(c_114326,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_113744,c_83524]) ).

tcf(c_114327,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_113744]) ).

tcf(c_114328,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_113419]) ).

tcf(c_114329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_112967]) ).

tcf(c_114330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_112089]) ).

tcf(c_114331,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_111767]) ).

tcf(c_114332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_111405]) ).

tcf(c_114333,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_111079]) ).

tcf(c_114334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_110591]) ).

tcf(c_114335,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_109784]) ).

tcf(c_114336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_109567]) ).

tcf(c_114337,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_108992]) ).

tcf(c_114338,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_107183]) ).

tcf(c_114342,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_106960]) ).

tcf(c_114343,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_105967]) ).

tcf(c_114345,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_95608]) ).

tcf(c_114348,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_113744,c_98014]) ).

tcf(c_114349,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_95414]) ).

tcf(c_114350,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_95286]) ).

tcf(c_114351,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_95041]) ).

tcf(c_114352,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_94695]) ).

tcf(c_114353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_94594]) ).

tcf(c_114354,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_93822]) ).

tcf(c_114355,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_93551]) ).

tcf(c_114356,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113744,c_79918]) ).

tcf(c_114359,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113744,c_83537]) ).

tcf(c_114360,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113744,c_83534]) ).

tcf(c_114366,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113744,c_96186]) ).

tcf(c_114367,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114254,c_59636]) ).

tcf(c_114368,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114249,c_79190]) ).

tcf(c_114369,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114356,c_76415]) ).

tcf(c_114370,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114257,c_76855,c_93903]) ).

tcf(c_114374,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_114348,c_79573]) ).

tcf(c_114659,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_92656]) ).

tcf(c_114660,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_113643,c_255]) ).

tcf(c_114662,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113643,c_256]) ).

tcf(c_114665,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_113643,c_83532]) ).

tcf(c_114666,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_113643,c_83524]) ).

tcf(c_114667,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_113744]) ).

tcf(c_114668,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_113419]) ).

tcf(c_114669,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_112967]) ).

tcf(c_114670,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_112089]) ).

tcf(c_114671,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_111767]) ).

tcf(c_114672,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_111405]) ).

tcf(c_114673,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_111079]) ).

tcf(c_114674,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_110591]) ).

tcf(c_114675,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_109784]) ).

tcf(c_114676,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_109567]) ).

tcf(c_114677,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_108992]) ).

tcf(c_114678,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_107183]) ).

tcf(c_114682,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_106960]) ).

tcf(c_114683,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_105967]) ).

tcf(c_114685,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_95608]) ).

tcf(c_114688,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_113643,c_98014]) ).

tcf(c_114689,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_95414]) ).

tcf(c_114690,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_95286]) ).

tcf(c_114691,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_95041]) ).

tcf(c_114692,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_94695]) ).

tcf(c_114693,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_94594]) ).

tcf(c_114694,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_93822]) ).

tcf(c_114695,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_93551]) ).

tcf(c_114696,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113643,c_79918]) ).

tcf(c_114699,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113643,c_83537]) ).

tcf(c_114700,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113643,c_83534]) ).

tcf(c_114706,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_113643,c_96186]) ).

tcf(c_114713,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_114688,c_79573]) ).

tcf(c_114785,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_114369]) ).

tcf(c_114786,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_114369]) ).

tcf(c_114787,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_114369]) ).

tcf(c_114788,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_114369]) ).

tcf(c_114790,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_114369]) ).

tcf(c_114791,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_114369]) ).

tcf(c_114793,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_114369]) ).

tcf(c_114794,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_114369]) ).

tcf(c_114795,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_114369]) ).

tcf(c_114796,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_114369]) ).

tcf(c_114797,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_114369]) ).

tcf(c_114798,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_114369]) ).

tcf(c_114799,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_114369]) ).

tcf(c_114800,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_114369]) ).

tcf(c_114801,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_114369]) ).

tcf(c_114802,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_114369]) ).

tcf(c_114803,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_114369]) ).

tcf(c_114804,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_114369]) ).

tcf(c_114805,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_114369]) ).

tcf(c_114806,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_114369]) ).

tcf(c_114807,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_114369]) ).

tcf(c_114808,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_114369]) ).

tcf(c_114809,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_114369]) ).

tcf(c_114810,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_114369]) ).

tcf(c_114811,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_114369]) ).

tcf(c_114812,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_114369]) ).

tcf(c_114813,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_114369]) ).

tcf(c_114814,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_114369]) ).

tcf(c_114815,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_114369]) ).

tcf(c_114816,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_114369]) ).

tcf(c_114817,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_114369]) ).

tcf(c_114818,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_114369]) ).

tcf(c_114819,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_114369]) ).

tcf(c_114820,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_114369]) ).

tcf(c_114821,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_114369]) ).

tcf(c_114822,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_114369]) ).

tcf(c_114823,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_114369]) ).

tcf(c_114824,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_114369]) ).

tcf(c_114825,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_114369]) ).

tcf(c_114826,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_114369]) ).

tcf(c_114827,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_114369]) ).

tcf(c_114828,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_114369]) ).

tcf(c_114829,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_114369]) ).

tcf(c_114830,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_114369]) ).

tcf(c_114831,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_114369]) ).

tcf(c_114832,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_114369]) ).

tcf(c_114833,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_114369]) ).

tcf(c_114834,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_114369]) ).

tcf(c_114835,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_114369]) ).

tcf(c_114836,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_114369]) ).

tcf(c_114837,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_114369]) ).

tcf(c_114838,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_114369]) ).

tcf(c_114839,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_114369]) ).

tcf(c_114840,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_114369]) ).

tcf(c_114841,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_114369]) ).

tcf(c_114842,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_114369]) ).

tcf(c_114843,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_114369]) ).

tcf(c_114844,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_114369]) ).

tcf(c_114845,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_114369]) ).

tcf(c_114846,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_114369]) ).

tcf(c_114847,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_114369]) ).

tcf(c_114848,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_114369]) ).

tcf(c_114849,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_114369]) ).

tcf(c_114850,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_114369]) ).

tcf(c_114851,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_114369]) ).

tcf(c_114852,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_114369]) ).

tcf(c_114853,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_114369]) ).

tcf(c_114854,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_114369]) ).

tcf(c_114857,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_92656]) ).

tcf(c_114858,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_114369,c_255]) ).

tcf(c_114860,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114369,c_256]) ).

tcf(c_114863,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_114369,c_83532]) ).

tcf(c_114864,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_114369,c_83524]) ).

tcf(c_114865,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_114369]) ).

tcf(c_114866,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_113744]) ).

tcf(c_114867,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_113419]) ).

tcf(c_114868,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_112967]) ).

tcf(c_114869,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_112089]) ).

tcf(c_114870,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_111767]) ).

tcf(c_114871,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_111405]) ).

tcf(c_114872,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_111079]) ).

tcf(c_114873,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_110591]) ).

tcf(c_114874,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_109784]) ).

tcf(c_114875,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_109567]) ).

tcf(c_114876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_108992]) ).

tcf(c_114877,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_107183]) ).

tcf(c_114881,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_106960]) ).

tcf(c_114882,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_105967]) ).

tcf(c_114884,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_95608]) ).

tcf(c_114887,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_114369,c_98014]) ).

tcf(c_114888,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_95414]) ).

tcf(c_114889,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_95286]) ).

tcf(c_114890,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_95041]) ).

tcf(c_114891,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_94695]) ).

tcf(c_114892,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_94594]) ).

tcf(c_114893,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_93822]) ).

tcf(c_114894,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_93551]) ).

tcf(c_114895,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114369,c_79918]) ).

tcf(c_114898,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114369,c_83537]) ).

tcf(c_114899,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114369,c_83534]) ).

tcf(c_114905,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114369,c_96186]) ).

tcf(c_114906,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114790,c_59636]) ).

tcf(c_114907,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114785,c_79190]) ).

tcf(c_114908,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114895,c_76415]) ).

tcf(c_114909,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_114793,c_76855,c_93903]) ).

tcf(c_114913,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_114887,c_79573]) ).

tcf(c_115143,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_92656]) ).

tcf(c_115144,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_114265,c_255]) ).

tcf(c_115146,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114265,c_256]) ).

tcf(c_115149,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_114265,c_83532]) ).

tcf(c_115150,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_114265,c_83524]) ).

tcf(c_115151,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_114369]) ).

tcf(c_115152,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_113744]) ).

tcf(c_115153,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_113419]) ).

tcf(c_115154,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_112967]) ).

tcf(c_115155,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_112089]) ).

tcf(c_115156,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_111767]) ).

tcf(c_115157,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_111405]) ).

tcf(c_115158,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_111079]) ).

tcf(c_115159,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_110591]) ).

tcf(c_115160,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_109784]) ).

tcf(c_115161,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_109567]) ).

tcf(c_115162,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_108992]) ).

tcf(c_115163,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_107183]) ).

tcf(c_115167,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_106960]) ).

tcf(c_115168,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_105967]) ).

tcf(c_115170,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_95608]) ).

tcf(c_115173,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_114265,c_98014]) ).

tcf(c_115174,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_95414]) ).

tcf(c_115175,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_95286]) ).

tcf(c_115176,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_95041]) ).

tcf(c_115177,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_94695]) ).

tcf(c_115178,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_94594]) ).

tcf(c_115179,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_93822]) ).

tcf(c_115180,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_93551]) ).

tcf(c_115181,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114265,c_79918]) ).

tcf(c_115184,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114265,c_83537]) ).

tcf(c_115185,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114265,c_83534]) ).

tcf(c_115191,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114265,c_96186]) ).

tcf(c_115198,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_115173,c_79573]) ).

tcf(c_115223,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_114908]) ).

tcf(c_115224,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_114908]) ).

tcf(c_115225,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_114908]) ).

tcf(c_115226,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_114908]) ).

tcf(c_115228,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_114908]) ).

tcf(c_115229,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_114908]) ).

tcf(c_115231,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_114908]) ).

tcf(c_115232,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_114908]) ).

tcf(c_115233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_114908]) ).

tcf(c_115234,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_114908]) ).

tcf(c_115235,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_114908]) ).

tcf(c_115236,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_114908]) ).

tcf(c_115237,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_114908]) ).

tcf(c_115238,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_114908]) ).

tcf(c_115239,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_114908]) ).

tcf(c_115240,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_114908]) ).

tcf(c_115241,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_114908]) ).

tcf(c_115242,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_114908]) ).

tcf(c_115243,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_114908]) ).

tcf(c_115244,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_114908]) ).

tcf(c_115245,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_114908]) ).

tcf(c_115246,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_114908]) ).

tcf(c_115247,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_114908]) ).

tcf(c_115248,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_114908]) ).

tcf(c_115249,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_114908]) ).

tcf(c_115250,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_114908]) ).

tcf(c_115251,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_114908]) ).

tcf(c_115252,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_114908]) ).

tcf(c_115253,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_114908]) ).

tcf(c_115254,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_114908]) ).

tcf(c_115255,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_114908]) ).

tcf(c_115256,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_114908]) ).

tcf(c_115257,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_114908]) ).

tcf(c_115258,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_114908]) ).

tcf(c_115259,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_114908]) ).

tcf(c_115260,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_114908]) ).

tcf(c_115261,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_114908]) ).

tcf(c_115262,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_114908]) ).

tcf(c_115263,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_114908]) ).

tcf(c_115264,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_114908]) ).

tcf(c_115265,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_114908]) ).

tcf(c_115266,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_114908]) ).

tcf(c_115267,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_114908]) ).

tcf(c_115268,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_114908]) ).

tcf(c_115269,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_114908]) ).

tcf(c_115270,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_114908]) ).

tcf(c_115271,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_114908]) ).

tcf(c_115272,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_114908]) ).

tcf(c_115273,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_114908]) ).

tcf(c_115274,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_114908]) ).

tcf(c_115275,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_114908]) ).

tcf(c_115276,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_114908]) ).

tcf(c_115277,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_114908]) ).

tcf(c_115278,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_114908]) ).

tcf(c_115279,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_114908]) ).

tcf(c_115280,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_114908]) ).

tcf(c_115281,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_114908]) ).

tcf(c_115282,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_114908]) ).

tcf(c_115283,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_114908]) ).

tcf(c_115284,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_114908]) ).

tcf(c_115285,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_114908]) ).

tcf(c_115286,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_114908]) ).

tcf(c_115287,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_114908]) ).

tcf(c_115288,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_114908]) ).

tcf(c_115289,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_114908]) ).

tcf(c_115290,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_114908]) ).

tcf(c_115291,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_114908]) ).

tcf(c_115292,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_114908]) ).

tcf(c_115293,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_114908]) ).

tcf(c_115294,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_114908]) ).

tcf(c_115297,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_92656]) ).

tcf(c_115298,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_114908,c_255]) ).

tcf(c_115300,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114908,c_256]) ).

tcf(c_115303,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_114908,c_83532]) ).

tcf(c_115304,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_114908,c_83524]) ).

tcf(c_115305,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_114908]) ).

tcf(c_115306,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_114369]) ).

tcf(c_115307,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_113744]) ).

tcf(c_115308,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_113419]) ).

tcf(c_115309,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_112967]) ).

tcf(c_115310,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_112089]) ).

tcf(c_115311,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_111767]) ).

tcf(c_115312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_111405]) ).

tcf(c_115313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_111079]) ).

tcf(c_115314,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_110591]) ).

tcf(c_115315,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_109784]) ).

tcf(c_115316,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_109567]) ).

tcf(c_115317,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_108992]) ).

tcf(c_115318,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_107183]) ).

tcf(c_115322,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_106960]) ).

tcf(c_115323,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_105967]) ).

tcf(c_115325,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_95608]) ).

tcf(c_115328,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_114908,c_98014]) ).

tcf(c_115329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_95414]) ).

tcf(c_115330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_95286]) ).

tcf(c_115331,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_95041]) ).

tcf(c_115332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_94695]) ).

tcf(c_115333,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_94594]) ).

tcf(c_115334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_93822]) ).

tcf(c_115335,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_93551]) ).

tcf(c_115336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114908,c_79918]) ).

tcf(c_115339,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114908,c_83537]) ).

tcf(c_115340,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114908,c_83534]) ).

tcf(c_115346,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114908,c_96186]) ).

tcf(c_115347,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115228,c_59636]) ).

tcf(c_115348,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115223,c_79190]) ).

tcf(c_115349,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115336,c_76415]) ).

tcf(c_115350,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115231,c_76855,c_93903]) ).

tcf(c_115354,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_115328,c_79573]) ).

tcf(c_115584,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_92656]) ).

tcf(c_115585,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_114801,c_255]) ).

tcf(c_115587,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114801,c_256]) ).

tcf(c_115590,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_114801,c_83532]) ).

tcf(c_115591,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_114801,c_83524]) ).

tcf(c_115592,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_114908]) ).

tcf(c_115593,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_114369]) ).

tcf(c_115594,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_113744]) ).

tcf(c_115595,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_113419]) ).

tcf(c_115596,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_112967]) ).

tcf(c_115597,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_112089]) ).

tcf(c_115598,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_111767]) ).

tcf(c_115599,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_111405]) ).

tcf(c_115600,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_111079]) ).

tcf(c_115601,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_110591]) ).

tcf(c_115602,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_109784]) ).

tcf(c_115603,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_109567]) ).

tcf(c_115604,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_108992]) ).

tcf(c_115605,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_107183]) ).

tcf(c_115609,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_106960]) ).

tcf(c_115610,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_105967]) ).

tcf(c_115612,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_95608]) ).

tcf(c_115615,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_114801,c_98014]) ).

tcf(c_115616,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_95414]) ).

tcf(c_115617,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_95286]) ).

tcf(c_115618,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_95041]) ).

tcf(c_115619,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_94695]) ).

tcf(c_115620,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_94594]) ).

tcf(c_115621,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_93822]) ).

tcf(c_115622,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_93551]) ).

tcf(c_115623,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114801,c_79918]) ).

tcf(c_115626,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114801,c_83537]) ).

tcf(c_115627,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114801,c_83534]) ).

tcf(c_115633,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_114801,c_96186]) ).

tcf(c_115640,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_115615,c_79573]) ).

tcf(c_115651,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_115349]) ).

tcf(c_115652,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_115349]) ).

tcf(c_115653,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_115349]) ).

tcf(c_115654,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_115349]) ).

tcf(c_115656,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_115349]) ).

tcf(c_115657,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_115349]) ).

tcf(c_115659,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_115349]) ).

tcf(c_115660,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_115349]) ).

tcf(c_115661,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_115349]) ).

tcf(c_115662,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_115349]) ).

tcf(c_115663,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_115349]) ).

tcf(c_115664,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_115349]) ).

tcf(c_115665,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_115349]) ).

tcf(c_115666,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_115349]) ).

tcf(c_115667,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_115349]) ).

tcf(c_115668,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_115349]) ).

tcf(c_115669,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_115349]) ).

tcf(c_115670,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_115349]) ).

tcf(c_115671,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_115349]) ).

tcf(c_115672,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_115349]) ).

tcf(c_115673,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_115349]) ).

tcf(c_115674,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_115349]) ).

tcf(c_115675,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_115349]) ).

tcf(c_115676,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_115349]) ).

tcf(c_115677,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_115349]) ).

tcf(c_115678,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_115349]) ).

tcf(c_115679,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_115349]) ).

tcf(c_115680,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_115349]) ).

tcf(c_115681,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_115349]) ).

tcf(c_115682,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_115349]) ).

tcf(c_115683,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_115349]) ).

tcf(c_115684,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_115349]) ).

tcf(c_115685,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_115349]) ).

tcf(c_115686,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_115349]) ).

tcf(c_115687,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_115349]) ).

tcf(c_115688,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_115349]) ).

tcf(c_115689,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_115349]) ).

tcf(c_115690,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_115349]) ).

tcf(c_115691,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_115349]) ).

tcf(c_115692,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_115349]) ).

tcf(c_115693,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_115349]) ).

tcf(c_115694,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_115349]) ).

tcf(c_115695,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_115349]) ).

tcf(c_115696,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_115349]) ).

tcf(c_115697,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_115349]) ).

tcf(c_115698,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_115349]) ).

tcf(c_115699,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_115349]) ).

tcf(c_115700,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_115349]) ).

tcf(c_115701,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_115349]) ).

tcf(c_115702,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_115349]) ).

tcf(c_115703,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_115349]) ).

tcf(c_115704,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_115349]) ).

tcf(c_115705,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_115349]) ).

tcf(c_115706,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_115349]) ).

tcf(c_115707,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_115349]) ).

tcf(c_115708,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_115349]) ).

tcf(c_115709,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_115349]) ).

tcf(c_115710,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_115349]) ).

tcf(c_115711,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_115349]) ).

tcf(c_115712,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_115349]) ).

tcf(c_115713,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_115349]) ).

tcf(c_115714,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_115349]) ).

tcf(c_115715,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_115349]) ).

tcf(c_115716,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_115349]) ).

tcf(c_115717,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_115349]) ).

tcf(c_115718,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_115349]) ).

tcf(c_115719,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_115349]) ).

tcf(c_115720,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_115349]) ).

tcf(c_115721,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_115349]) ).

tcf(c_115722,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_115349]) ).

tcf(c_115723,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_115349]) ).

tcf(c_115724,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_115349]) ).

tcf(c_115727,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_92656]) ).

tcf(c_115728,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_115349,c_255]) ).

tcf(c_115730,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115349,c_256]) ).

tcf(c_115733,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_115349,c_83532]) ).

tcf(c_115734,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_115349,c_83524]) ).

tcf(c_115735,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_115349]) ).

tcf(c_115736,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_114908]) ).

tcf(c_115737,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_114369]) ).

tcf(c_115738,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_113744]) ).

tcf(c_115739,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_113419]) ).

tcf(c_115740,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_112967]) ).

tcf(c_115741,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_112089]) ).

tcf(c_115742,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_111767]) ).

tcf(c_115743,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_111405]) ).

tcf(c_115744,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_111079]) ).

tcf(c_115745,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_110591]) ).

tcf(c_115746,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_109784]) ).

tcf(c_115747,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_109567]) ).

tcf(c_115748,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_108992]) ).

tcf(c_115749,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_107183]) ).

tcf(c_115753,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_106960]) ).

tcf(c_115754,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_105967]) ).

tcf(c_115756,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_95608]) ).

tcf(c_115759,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_115349,c_98014]) ).

tcf(c_115760,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_95414]) ).

tcf(c_115761,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_95286]) ).

tcf(c_115762,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_95041]) ).

tcf(c_115763,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_94695]) ).

tcf(c_115764,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_94594]) ).

tcf(c_115765,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_93822]) ).

tcf(c_115766,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_93551]) ).

tcf(c_115767,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115349,c_79918]) ).

tcf(c_115770,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115349,c_83537]) ).

tcf(c_115771,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115349,c_83534]) ).

tcf(c_115777,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115349,c_96186]) ).

tcf(c_115778,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115656,c_59636]) ).

tcf(c_115779,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115651,c_79190]) ).

tcf(c_115780,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115767,c_76415]) ).

tcf(c_115781,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_115659,c_76855,c_93903]) ).

tcf(c_115785,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_115759,c_79573]) ).

tcf(c_116236,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_92656]) ).

tcf(c_116237,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_115239,c_255]) ).

tcf(c_116239,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115239,c_256]) ).

tcf(c_116242,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_115239,c_83532]) ).

tcf(c_116243,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_115239,c_83524]) ).

tcf(c_116244,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_115349]) ).

tcf(c_116245,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_114908]) ).

tcf(c_116246,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_114369]) ).

tcf(c_116247,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_113744]) ).

tcf(c_116248,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_113419]) ).

tcf(c_116249,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_112967]) ).

tcf(c_116250,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_112089]) ).

tcf(c_116251,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_111767]) ).

tcf(c_116252,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_111405]) ).

tcf(c_116253,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_111079]) ).

tcf(c_116254,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_110591]) ).

tcf(c_116255,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_109784]) ).

tcf(c_116256,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_109567]) ).

tcf(c_116257,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_108992]) ).

tcf(c_116258,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_107183]) ).

tcf(c_116262,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_106960]) ).

tcf(c_116263,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_105967]) ).

tcf(c_116265,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_95608]) ).

tcf(c_116268,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_115239,c_98014]) ).

tcf(c_116269,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_95414]) ).

tcf(c_116270,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_95286]) ).

tcf(c_116271,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_95041]) ).

tcf(c_116272,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_94695]) ).

tcf(c_116273,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_94594]) ).

tcf(c_116274,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_93822]) ).

tcf(c_116275,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_93551]) ).

tcf(c_116276,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115239,c_79918]) ).

tcf(c_116279,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115239,c_83537]) ).

tcf(c_116280,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115239,c_83534]) ).

tcf(c_116286,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115239,c_96186]) ).

tcf(c_116293,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_116268,c_79573]) ).

tcf(c_116338,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_84385,c_91937]) ).

tcf(c_116339,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_253,c_116338]) ).

tcf(c_116341,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls)),
    inference(superposition,[status(thm)],[c_574,c_116338]) ).

tcf(c_116342,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min)),
    inference(superposition,[status(thm)],[c_76397,c_116338]) ).

tcf(c_116343,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_116338]) ).

tcf(c_116344,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_116338]) ).

tcf(c_116345,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_76399,c_116338]) ).

tcf(c_116346,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_76401,c_116338]) ).

tcf(c_116347,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m)),
    inference(superposition,[status(thm)],[c_76402,c_116338]) ).

tcf(c_116348,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1)),
    inference(superposition,[status(thm)],[c_76403,c_116338]) ).

tcf(c_116349,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s)),
    inference(superposition,[status(thm)],[c_76404,c_116338]) ).

tcf(c_116350,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t)),
    inference(superposition,[status(thm)],[c_76405,c_116338]) ).

tcf(c_116351,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_116338]) ).

tcf(c_116352,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_116338]) ).

tcf(c_116353,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_116338]) ).

tcf(c_116354,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_116338]) ).

tcf(c_116355,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_116338]) ).

tcf(c_116356,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_116338]) ).

tcf(c_116357,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_116338]) ).

tcf(c_116358,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_116338]) ).

tcf(c_116359,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_116338]) ).

tcf(c_116360,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_116338]) ).

tcf(c_116361,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_77366,c_116338]) ).

tcf(c_116362,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0))),
    inference(superposition,[status(thm)],[c_78024,c_116338]) ).

tcf(c_116363,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t))),
    inference(superposition,[status(thm)],[c_78042,c_116338]) ).

tcf(c_116364,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_116338]) ).

tcf(c_116365,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_116338]) ).

tcf(c_116367,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_116338]) ).

tcf(c_116369,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_116338]) ).

tcf(c_116370,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_116338]) ).

tcf(c_116372,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_116338]) ).

tcf(c_116373,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_116338]) ).

tcf(c_116374,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_116338]) ).

tcf(c_116375,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_116338]) ).

tcf(c_116376,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_116338]) ).

tcf(c_116377,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_116338]) ).

tcf(c_116378,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_116338]) ).

tcf(c_116379,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96714,c_116338]) ).

tcf(c_116380,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_99171,c_116338]) ).

tcf(c_116381,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_116338]) ).

tcf(c_116382,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_116338]) ).

tcf(c_116384,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_116338,c_92656]) ).

tcf(c_116385,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),X1),
    inference(superposition,[status(thm)],[c_116338,c_255]) ).

tcf(c_116387,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1)))),
    inference(superposition,[status(thm)],[c_116338,c_256]) ).

tcf(c_116389,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m),
    inference(light_normalisation,[status(thm)],[c_116341,c_77414]) ).

tcf(c_116732,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_79150,c_45998]) ).

tcf(c_116734,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_255,c_45998]) ).

tcf(c_116735,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_256,c_45998]) ).

tcf(c_116738,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_388,c_45998]) ).

tcf(c_116739,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,m),pls)) ),
    inference(superposition,[status(thm)],[c_79190,c_45998]) ).

tcf(c_116741,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),cOMBC_int_int_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_45998,c_226]) ).

tcf(c_116748,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
    inference(light_normalisation,[status(thm)],[c_116738,c_79988]) ).

tcf(c_116751,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(light_normalisation,[status(thm)],[c_116735,c_92971]) ).

tcf(c_116790,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_79150,c_46002]) ).

tcf(c_116792,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_255,c_46002]) ).

tcf(c_116793,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_256,c_46002]) ).

tcf(c_116796,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(superposition,[status(thm)],[c_388,c_46002]) ).

tcf(c_116797,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_13,iPr_def_14)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),pls)) ),
    inference(superposition,[status(thm)],[c_79190,c_46002]) ).

tcf(c_116798,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(iPr_def_12,one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_59636,c_46002]) ).

tcf(c_116799,plain,
    ! [X0: $i] :
      ( hBOOL(member_int(hAPP_int_int(plus_plus_int(X0),X0),cOMBC_int_int_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_46002,c_226]) ).

tcf(c_116800,plain,
    ! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X0)),pls)),
    inference(superposition,[status(thm)],[c_46002,c_12163]) ).

tcf(c_116801,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),iPr_def_14))
    | ~ hBOOL(hAPP_int_bool(iPr_def_19,pls)) ),
    inference(light_normalisation,[status(thm)],[c_116798,c_59638,c_59643]) ).

tcf(c_116808,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
    inference(light_normalisation,[status(thm)],[c_116796,c_79988]) ).

tcf(c_116811,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(iPr_def_14),hAPP_int_int(plus_plus_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X0),X1)),pls)) ),
    inference(light_normalisation,[status(thm)],[c_116793,c_92971]) ).

tcf(c_116823,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)) ),
    inference(superposition,[status(thm)],[c_76437,c_46130]) ).

tcf(c_116825,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK30(iPr_def_19)),pls)) ),
    inference(superposition,[status(thm)],[c_83483,c_46130]) ).

tcf(c_116827,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
    inference(superposition,[status(thm)],[c_84522,c_46130]) ).

tcf(c_116828,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,iPr_def_16),pls)) ),
    inference(superposition,[status(thm)],[c_84527,c_46130]) ).

tcf(c_116829,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m),pls)) ),
    inference(superposition,[status(thm)],[c_84528,c_46130]) ).

tcf(c_116834,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_92002,c_46130]) ).

tcf(c_116835,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_98912,c_46130]) ).

tcf(c_116839,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(div_mod_int(X1),X0),cOMBC_int_int_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_46130,c_226]) ).

tcf(c_116846,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(iPr_def_19,pls)) ),
    inference(light_normalisation,[status(thm)],[c_116827,c_59643]) ).

tcf(c_116861,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))) ),
    inference(superposition,[status(thm)],[c_82983,c_46144]) ).

tcf(c_116862,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) ),
    inference(superposition,[status(thm)],[c_83483,c_46144]) ).

tcf(c_116863,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))) ),
    inference(superposition,[status(thm)],[c_83484,c_46144]) ).

tcf(c_116864,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_84522,c_46144]) ).

tcf(c_116867,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))) ),
    inference(superposition,[status(thm)],[c_85345,c_46144]) ).

tcf(c_116868,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_88495,c_46144]) ).

tcf(c_116869,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X1),sK30(iPr_def_19),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_88514,c_46144]) ).

tcf(c_116870,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_88551,c_46144]) ).

tcf(c_116871,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK30(iPr_def_19))))) ),
    inference(superposition,[status(thm)],[c_92002,c_46144]) ).

tcf(c_116872,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2))))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X2)))))) ),
    inference(superposition,[status(thm)],[c_98912,c_46144]) ).

tcf(c_116873,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m)))))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),m))))))) ),
    inference(superposition,[status(thm)],[c_99038,c_46144]) ).

tcf(c_116874,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1))))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X1)))))) ),
    inference(superposition,[status(thm)],[c_108222,c_46144]) ).

tcf(c_116875,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))) ),
    inference(superposition,[status(thm)],[c_108794,c_46144]) ).

tcf(c_116876,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(div_mod_int(X0),X1),cOMBC_int_int_bool(ord_less_eq_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_46144,c_226]) ).

tcf(c_116885,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),pls)),
    inference(forward_subsumption_resolution,[status(thm)],[c_116862,c_78970]) ).

tcf(c_116918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),X0)) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_46106]) ).

tcf(c_116919,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,s1),s1,s1))),X0) = pls,
    inference(superposition,[status(thm)],[c_114248,c_46104]) ).

tcf(c_116920,plain,
    hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),pls) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_880]) ).

tcf(c_116921,plain,
    hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_608]) ).

tcf(c_116922,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),pls) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_524]) ).

tcf(c_116923,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_523]) ).

tcf(c_116924,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_347]) ).

tcf(c_116925,plain,
    hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)),one_one_int) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_346]) ).

tcf(c_116926,plain,
    number_number_of_int(sK14(hAPP_int_int(iPr_def_13,s1),s1,s1)) = sK14(hAPP_int_int(iPr_def_13,s1),s1,s1),
    inference(superposition,[status(thm)],[c_114248,c_254]) ).

tcf(c_116972,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(s,hAPP_int_int(times_times_int(s),X0)),s)),
    inference(superposition,[status(thm)],[c_253,c_78306]) ).

tcf(c_116974,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(s,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),s))),s)),
    inference(superposition,[status(thm)],[c_252,c_78306]) ).

tcf(c_116975,plain,
    hBOOL(hAPP_int_bool(zcong(s,pls),s)),
    inference(superposition,[status(thm)],[c_1004,c_78306]) ).

tcf(c_116976,plain,
    hBOOL(hAPP_int_bool(zcong(s,hAPP_int_int(plus_plus_int(s),s)),s)),
    inference(superposition,[status(thm)],[c_79150,c_78306]) ).

tcf(c_116977,plain,
    hBOOL(hAPP_int_bool(zcong(s,hAPP_int_int(iPr_def_13,s)),s)),
    inference(superposition,[status(thm)],[c_59637,c_78306]) ).

tcf(c_116978,plain,
    ! [X0: $i] : hBOOL(member_int(s,zcong(s,hAPP_int_int(times_times_int(X0),s)))),
    inference(superposition,[status(thm)],[c_78306,c_226]) ).

tcf(c_116979,plain,
    ! [X0: $i] :
      ( is_int(sK14(s,hAPP_int_int(times_times_int(X0),s),s))
      | ~ is_int(hAPP_int_int(times_times_int(X0),s)) ),
    inference(superposition,[status(thm)],[c_78306,c_852]) ).

tcf(c_116987,plain,
    hBOOL(member_int(s,zcong(s,hAPP_int_int(iPr_def_13,s)))),
    inference(superposition,[status(thm)],[c_116977,c_226]) ).

tcf(c_116988,plain,
    ( is_int(sK14(s,hAPP_int_int(iPr_def_13,s),s))
    | ~ is_int(hAPP_int_int(iPr_def_13,s)) ),
    inference(superposition,[status(thm)],[c_116977,c_852]) ).

tcf(c_116989,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,s),s),s)),
    inference(superposition,[status(thm)],[c_116977,c_814]) ).

tcf(c_116990,plain,
    is_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),
    inference(forward_subsumption_resolution,[status(thm)],[c_116988,c_77054]) ).

tcf(c_116992,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_116360,c_253]) ).

tcf(c_116994,plain,
    hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_116992,c_92656]) ).

tcf(c_116995,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0),
    inference(superposition,[status(thm)],[c_116992,c_255]) ).

tcf(c_116996,plain,
    ( is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))
    | ~ is_int(pls) ),
    inference(superposition,[status(thm)],[c_116992,c_76880]) ).

tcf(c_116997,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(superposition,[status(thm)],[c_116992,c_256]) ).

tcf(c_116999,plain,
    is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),
    inference(forward_subsumption_resolution,[status(thm)],[c_116996,c_57]) ).

tcf(c_117002,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_115780]) ).

tcf(c_117003,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_115780]) ).

tcf(c_117004,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_115780]) ).

tcf(c_117005,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_115780]) ).

tcf(c_117007,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_115780]) ).

tcf(c_117008,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_115780]) ).

tcf(c_117010,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_115780]) ).

tcf(c_117011,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_115780]) ).

tcf(c_117012,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_115780]) ).

tcf(c_117013,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_115780]) ).

tcf(c_117014,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_115780]) ).

tcf(c_117015,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_115780]) ).

tcf(c_117016,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_115780]) ).

tcf(c_117017,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_115780]) ).

tcf(c_117018,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_115780]) ).

tcf(c_117019,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_115780]) ).

tcf(c_117020,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_115780]) ).

tcf(c_117021,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_115780]) ).

tcf(c_117022,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_115780]) ).

tcf(c_117023,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_115780]) ).

tcf(c_117024,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_115780]) ).

tcf(c_117025,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_115780]) ).

tcf(c_117026,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_115780]) ).

tcf(c_117027,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_115780]) ).

tcf(c_117028,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_115780]) ).

tcf(c_117029,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_115780]) ).

tcf(c_117030,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_115780]) ).

tcf(c_117031,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_115780]) ).

tcf(c_117032,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_115780]) ).

tcf(c_117033,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_115780]) ).

tcf(c_117034,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_115780]) ).

tcf(c_117035,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_115780]) ).

tcf(c_117036,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_115780]) ).

tcf(c_117037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_115780]) ).

tcf(c_117038,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_115780]) ).

tcf(c_117039,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_115780]) ).

tcf(c_117040,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_115780]) ).

tcf(c_117041,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_115780]) ).

tcf(c_117042,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_115780]) ).

tcf(c_117043,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_115780]) ).

tcf(c_117044,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_115780]) ).

tcf(c_117045,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_115780]) ).

tcf(c_117046,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_115780]) ).

tcf(c_117047,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_115780]) ).

tcf(c_117048,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_115780]) ).

tcf(c_117049,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_115780]) ).

tcf(c_117050,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_115780]) ).

tcf(c_117051,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_115780]) ).

tcf(c_117052,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_115780]) ).

tcf(c_117053,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_115780]) ).

tcf(c_117054,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_115780]) ).

tcf(c_117055,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_115780]) ).

tcf(c_117056,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_115780]) ).

tcf(c_117057,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_115780]) ).

tcf(c_117058,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_115780]) ).

tcf(c_117059,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_115780]) ).

tcf(c_117060,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_115780]) ).

tcf(c_117061,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_115780]) ).

tcf(c_117062,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_115780]) ).

tcf(c_117063,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_115780]) ).

tcf(c_117064,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_115780]) ).

tcf(c_117065,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_115780]) ).

tcf(c_117066,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_115780]) ).

tcf(c_117067,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_115780]) ).

tcf(c_117068,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_115780]) ).

tcf(c_117069,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_115780]) ).

tcf(c_117070,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_115780]) ).

tcf(c_117071,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_115780]) ).

tcf(c_117072,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_115780]) ).

tcf(c_117073,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_115780]) ).

tcf(c_117074,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_115780]) ).

tcf(c_117075,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_115780]) ).

tcf(c_117076,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_115780]) ).

tcf(c_117077,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_115780]) ).

tcf(c_117080,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_92656]) ).

tcf(c_117081,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_115780,c_255]) ).

tcf(c_117083,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115780,c_256]) ).

tcf(c_117086,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_115780,c_83532]) ).

tcf(c_117087,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_115780,c_83524]) ).

tcf(c_117088,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_115780]) ).

tcf(c_117089,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_115349]) ).

tcf(c_117090,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_114908]) ).

tcf(c_117091,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_114369]) ).

tcf(c_117092,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_113744]) ).

tcf(c_117093,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_113419]) ).

tcf(c_117094,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_112967]) ).

tcf(c_117095,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_112089]) ).

tcf(c_117096,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_111767]) ).

tcf(c_117097,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_111405]) ).

tcf(c_117098,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_111079]) ).

tcf(c_117099,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_110591]) ).

tcf(c_117100,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_109784]) ).

tcf(c_117101,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_109567]) ).

tcf(c_117102,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_108992]) ).

tcf(c_117103,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_107183]) ).

tcf(c_117107,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_106960]) ).

tcf(c_117108,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_105967]) ).

tcf(c_117110,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_95608]) ).

tcf(c_117113,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_115780,c_98014]) ).

tcf(c_117114,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_95414]) ).

tcf(c_117115,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_95286]) ).

tcf(c_117116,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_95041]) ).

tcf(c_117117,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_94695]) ).

tcf(c_117118,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_94594]) ).

tcf(c_117119,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_93822]) ).

tcf(c_117120,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_93551]) ).

tcf(c_117121,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115780,c_79918]) ).

tcf(c_117124,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115780,c_83537]) ).

tcf(c_117125,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115780,c_83534]) ).

tcf(c_117131,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115780,c_96186]) ).

tcf(c_117132,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117007,c_59636]) ).

tcf(c_117133,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117002,c_79190]) ).

tcf(c_117134,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117121,c_76415]) ).

tcf(c_117135,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117010,c_76855,c_93903]) ).

tcf(c_117139,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_117113,c_79573]) ).

tcf(c_117741,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_92656]) ).

tcf(c_117742,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_115667,c_255]) ).

tcf(c_117744,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115667,c_256]) ).

tcf(c_117747,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_115667,c_83532]) ).

tcf(c_117748,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_115667,c_83524]) ).

tcf(c_117749,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_115780]) ).

tcf(c_117750,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_115349]) ).

tcf(c_117751,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_114908]) ).

tcf(c_117752,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_114369]) ).

tcf(c_117753,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_113744]) ).

tcf(c_117754,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_113419]) ).

tcf(c_117755,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_112967]) ).

tcf(c_117756,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_112089]) ).

tcf(c_117757,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_111767]) ).

tcf(c_117758,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_111405]) ).

tcf(c_117759,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_111079]) ).

tcf(c_117760,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_110591]) ).

tcf(c_117761,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_109784]) ).

tcf(c_117762,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_109567]) ).

tcf(c_117763,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_108992]) ).

tcf(c_117764,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_107183]) ).

tcf(c_117768,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_106960]) ).

tcf(c_117769,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_105967]) ).

tcf(c_117771,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_95608]) ).

tcf(c_117774,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_115667,c_98014]) ).

tcf(c_117775,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_95414]) ).

tcf(c_117776,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_95286]) ).

tcf(c_117777,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_95041]) ).

tcf(c_117778,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_94695]) ).

tcf(c_117779,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_94594]) ).

tcf(c_117780,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_93822]) ).

tcf(c_117781,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_93551]) ).

tcf(c_117782,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115667,c_79918]) ).

tcf(c_117785,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115667,c_83537]) ).

tcf(c_117786,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115667,c_83534]) ).

tcf(c_117792,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_115667,c_96186]) ).

tcf(c_117799,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_117774,c_79573]) ).

tcf(c_117845,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_117134]) ).

tcf(c_117846,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_117134]) ).

tcf(c_117847,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_117134]) ).

tcf(c_117848,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_117134]) ).

tcf(c_117850,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_117134]) ).

tcf(c_117851,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_117134]) ).

tcf(c_117853,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_117134]) ).

tcf(c_117854,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_117134]) ).

tcf(c_117855,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_117134]) ).

tcf(c_117856,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_117134]) ).

tcf(c_117857,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_117134]) ).

tcf(c_117858,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_117134]) ).

tcf(c_117859,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_117134]) ).

tcf(c_117860,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_117134]) ).

tcf(c_117861,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_117134]) ).

tcf(c_117862,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_117134]) ).

tcf(c_117863,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_117134]) ).

tcf(c_117864,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_117134]) ).

tcf(c_117865,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_117134]) ).

tcf(c_117866,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_117134]) ).

tcf(c_117867,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_117134]) ).

tcf(c_117868,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_117134]) ).

tcf(c_117869,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_117134]) ).

tcf(c_117870,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_117134]) ).

tcf(c_117871,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_117134]) ).

tcf(c_117872,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_117134]) ).

tcf(c_117873,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_117134]) ).

tcf(c_117874,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_117134]) ).

tcf(c_117875,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_117134]) ).

tcf(c_117876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_117134]) ).

tcf(c_117877,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_117134]) ).

tcf(c_117878,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_117134]) ).

tcf(c_117879,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_117134]) ).

tcf(c_117880,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_117134]) ).

tcf(c_117881,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_117134]) ).

tcf(c_117882,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_117134]) ).

tcf(c_117883,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_117134]) ).

tcf(c_117884,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_117134]) ).

tcf(c_117885,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_117134]) ).

tcf(c_117886,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_117134]) ).

tcf(c_117887,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_117134]) ).

tcf(c_117888,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_117134]) ).

tcf(c_117889,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_117134]) ).

tcf(c_117890,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_117134]) ).

tcf(c_117891,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_117134]) ).

tcf(c_117892,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_117134]) ).

tcf(c_117893,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_117134]) ).

tcf(c_117894,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_117134]) ).

tcf(c_117895,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_117134]) ).

tcf(c_117896,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_117134]) ).

tcf(c_117897,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_117134]) ).

tcf(c_117898,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_117134]) ).

tcf(c_117899,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_117134]) ).

tcf(c_117900,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_117134]) ).

tcf(c_117901,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_117134]) ).

tcf(c_117902,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_117134]) ).

tcf(c_117903,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_117134]) ).

tcf(c_117904,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_117134]) ).

tcf(c_117905,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_117134]) ).

tcf(c_117906,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_117134]) ).

tcf(c_117907,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_117134]) ).

tcf(c_117908,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_117134]) ).

tcf(c_117909,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_117134]) ).

tcf(c_117910,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_117134]) ).

tcf(c_117911,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_117134]) ).

tcf(c_117912,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_117134]) ).

tcf(c_117913,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_117134]) ).

tcf(c_117914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_117134]) ).

tcf(c_117915,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_117134]) ).

tcf(c_117916,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_117134]) ).

tcf(c_117917,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_117134]) ).

tcf(c_117918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_117134]) ).

tcf(c_117919,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_117134]) ).

tcf(c_117920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_117134]) ).

tcf(c_117921,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_117134]) ).

tcf(c_117922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_117134]) ).

tcf(c_117925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_92656]) ).

tcf(c_117926,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_117134,c_255]) ).

tcf(c_117928,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117134,c_256]) ).

tcf(c_117931,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_117134,c_83532]) ).

tcf(c_117932,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_117134,c_83524]) ).

tcf(c_117933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_117134]) ).

tcf(c_117934,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_115780]) ).

tcf(c_117935,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_115349]) ).

tcf(c_117936,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_114908]) ).

tcf(c_117937,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_114369]) ).

tcf(c_117938,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_113744]) ).

tcf(c_117939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_113419]) ).

tcf(c_117940,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_112967]) ).

tcf(c_117941,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_112089]) ).

tcf(c_117942,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_111767]) ).

tcf(c_117943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_111405]) ).

tcf(c_117944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_111079]) ).

tcf(c_117945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_110591]) ).

tcf(c_117946,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_109784]) ).

tcf(c_117947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_109567]) ).

tcf(c_117948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_108992]) ).

tcf(c_117949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_107183]) ).

tcf(c_117953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_106960]) ).

tcf(c_117954,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_105967]) ).

tcf(c_117956,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_95608]) ).

tcf(c_117959,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_117134,c_98014]) ).

tcf(c_117960,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_95414]) ).

tcf(c_117961,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_95286]) ).

tcf(c_117962,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_95041]) ).

tcf(c_117963,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_94695]) ).

tcf(c_117964,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_94594]) ).

tcf(c_117965,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_93822]) ).

tcf(c_117966,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_93551]) ).

tcf(c_117967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117134,c_79918]) ).

tcf(c_117970,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117134,c_83537]) ).

tcf(c_117971,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117134,c_83534]) ).

tcf(c_117977,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117134,c_96186]) ).

tcf(c_117978,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117850,c_59636]) ).

tcf(c_117979,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117845,c_79190]) ).

tcf(c_117980,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117967,c_76415]) ).

tcf(c_117981,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_117853,c_76855,c_93903]) ).

tcf(c_117985,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_117959,c_79573]) ).

tcf(c_118193,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_92656]) ).

tcf(c_118194,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_117018,c_255]) ).

tcf(c_118196,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117018,c_256]) ).

tcf(c_118199,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_117018,c_83532]) ).

tcf(c_118200,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_117018,c_83524]) ).

tcf(c_118201,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_117134]) ).

tcf(c_118202,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_115780]) ).

tcf(c_118203,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_115349]) ).

tcf(c_118204,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_114908]) ).

tcf(c_118205,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_114369]) ).

tcf(c_118206,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_113744]) ).

tcf(c_118207,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_113419]) ).

tcf(c_118208,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_112967]) ).

tcf(c_118209,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_112089]) ).

tcf(c_118210,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_111767]) ).

tcf(c_118211,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_111405]) ).

tcf(c_118212,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_111079]) ).

tcf(c_118213,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_110591]) ).

tcf(c_118214,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_109784]) ).

tcf(c_118215,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_109567]) ).

tcf(c_118216,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_108992]) ).

tcf(c_118217,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_107183]) ).

tcf(c_118221,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_106960]) ).

tcf(c_118222,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_105967]) ).

tcf(c_118224,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_95608]) ).

tcf(c_118227,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_117018,c_98014]) ).

tcf(c_118228,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_95414]) ).

tcf(c_118229,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_95286]) ).

tcf(c_118230,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_95041]) ).

tcf(c_118231,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_94695]) ).

tcf(c_118232,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_94594]) ).

tcf(c_118233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_93822]) ).

tcf(c_118234,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_93551]) ).

tcf(c_118235,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117018,c_79918]) ).

tcf(c_118238,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117018,c_83537]) ).

tcf(c_118239,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117018,c_83534]) ).

tcf(c_118245,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117018,c_96186]) ).

tcf(c_118252,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_118227,c_79573]) ).

tcf(c_118284,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_117980]) ).

tcf(c_118285,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_117980]) ).

tcf(c_118286,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_117980]) ).

tcf(c_118287,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_117980]) ).

tcf(c_118289,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_117980]) ).

tcf(c_118290,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_117980]) ).

tcf(c_118292,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_117980]) ).

tcf(c_118293,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_117980]) ).

tcf(c_118294,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_117980]) ).

tcf(c_118295,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_117980]) ).

tcf(c_118296,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_117980]) ).

tcf(c_118297,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_117980]) ).

tcf(c_118298,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_117980]) ).

tcf(c_118299,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_117980]) ).

tcf(c_118300,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_117980]) ).

tcf(c_118301,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_117980]) ).

tcf(c_118302,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_117980]) ).

tcf(c_118303,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_117980]) ).

tcf(c_118304,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_117980]) ).

tcf(c_118305,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_117980]) ).

tcf(c_118306,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_117980]) ).

tcf(c_118307,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_117980]) ).

tcf(c_118308,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_117980]) ).

tcf(c_118309,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_117980]) ).

tcf(c_118310,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_117980]) ).

tcf(c_118311,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_117980]) ).

tcf(c_118312,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_117980]) ).

tcf(c_118313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_117980]) ).

tcf(c_118314,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_117980]) ).

tcf(c_118315,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_117980]) ).

tcf(c_118316,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_117980]) ).

tcf(c_118317,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_117980]) ).

tcf(c_118318,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_117980]) ).

tcf(c_118319,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_117980]) ).

tcf(c_118320,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_117980]) ).

tcf(c_118321,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_117980]) ).

tcf(c_118322,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_117980]) ).

tcf(c_118323,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_117980]) ).

tcf(c_118324,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_117980]) ).

tcf(c_118325,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_117980]) ).

tcf(c_118326,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_117980]) ).

tcf(c_118327,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_117980]) ).

tcf(c_118328,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_117980]) ).

tcf(c_118329,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_117980]) ).

tcf(c_118330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_117980]) ).

tcf(c_118331,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_117980]) ).

tcf(c_118332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_117980]) ).

tcf(c_118333,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_117980]) ).

tcf(c_118334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_117980]) ).

tcf(c_118335,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_117980]) ).

tcf(c_118336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_117980]) ).

tcf(c_118337,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_117980]) ).

tcf(c_118338,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_117980]) ).

tcf(c_118339,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_117980]) ).

tcf(c_118340,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_117980]) ).

tcf(c_118341,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_117980]) ).

tcf(c_118342,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_117980]) ).

tcf(c_118343,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_117980]) ).

tcf(c_118344,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_117980]) ).

tcf(c_118345,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_117980]) ).

tcf(c_118346,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_117980]) ).

tcf(c_118347,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_117980]) ).

tcf(c_118348,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_117980]) ).

tcf(c_118349,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_117980]) ).

tcf(c_118350,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_117980]) ).

tcf(c_118351,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_117980]) ).

tcf(c_118352,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_117980]) ).

tcf(c_118353,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_117980]) ).

tcf(c_118354,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_117980]) ).

tcf(c_118355,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_117980]) ).

tcf(c_118356,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_117980]) ).

tcf(c_118357,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_117980]) ).

tcf(c_118358,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_117980]) ).

tcf(c_118359,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_117980]) ).

tcf(c_118360,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_117980]) ).

tcf(c_118361,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_117980]) ).

tcf(c_118362,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_117980]) ).

tcf(c_118363,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_117980]) ).

tcf(c_118366,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_92656]) ).

tcf(c_118367,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_117980,c_255]) ).

tcf(c_118369,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117980,c_256]) ).

tcf(c_118372,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_117980,c_83532]) ).

tcf(c_118373,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_117980,c_83524]) ).

tcf(c_118374,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_117980]) ).

tcf(c_118375,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_117134]) ).

tcf(c_118376,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_115780]) ).

tcf(c_118377,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_115349]) ).

tcf(c_118378,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_114908]) ).

tcf(c_118379,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_114369]) ).

tcf(c_118380,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_113744]) ).

tcf(c_118381,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_113419]) ).

tcf(c_118382,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_112967]) ).

tcf(c_118383,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_112089]) ).

tcf(c_118384,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_111767]) ).

tcf(c_118385,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_111405]) ).

tcf(c_118386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_111079]) ).

tcf(c_118387,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_110591]) ).

tcf(c_118388,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_109784]) ).

tcf(c_118389,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_109567]) ).

tcf(c_118390,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_108992]) ).

tcf(c_118391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_107183]) ).

tcf(c_118395,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_106960]) ).

tcf(c_118396,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_105967]) ).

tcf(c_118398,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_95608]) ).

tcf(c_118401,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_117980,c_98014]) ).

tcf(c_118402,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_95414]) ).

tcf(c_118403,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_95286]) ).

tcf(c_118404,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_95041]) ).

tcf(c_118405,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_94695]) ).

tcf(c_118406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_94594]) ).

tcf(c_118407,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_93822]) ).

tcf(c_118408,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_93551]) ).

tcf(c_118409,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117980,c_79918]) ).

tcf(c_118412,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117980,c_83537]) ).

tcf(c_118413,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117980,c_83534]) ).

tcf(c_118419,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117980,c_96186]) ).

tcf(c_118420,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_118289,c_59636]) ).

tcf(c_118421,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_118284,c_79190]) ).

tcf(c_118422,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_118409,c_76415]) ).

tcf(c_118423,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_118292,c_76855,c_93903]) ).

tcf(c_118427,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_118401,c_79573]) ).

tcf(c_118696,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_92656]) ).

tcf(c_118697,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_117861,c_255]) ).

tcf(c_118699,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117861,c_256]) ).

tcf(c_118702,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_117861,c_83532]) ).

tcf(c_118703,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_117861,c_83524]) ).

tcf(c_118704,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_117980]) ).

tcf(c_118705,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_117134]) ).

tcf(c_118706,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_115780]) ).

tcf(c_118707,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_115349]) ).

tcf(c_118708,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_114908]) ).

tcf(c_118709,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_114369]) ).

tcf(c_118710,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_113744]) ).

tcf(c_118711,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_113419]) ).

tcf(c_118712,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_112967]) ).

tcf(c_118713,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_112089]) ).

tcf(c_118714,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_111767]) ).

tcf(c_118715,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_111405]) ).

tcf(c_118716,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_111079]) ).

tcf(c_118717,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_110591]) ).

tcf(c_118718,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_109784]) ).

tcf(c_118719,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_109567]) ).

tcf(c_118720,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_108992]) ).

tcf(c_118721,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_107183]) ).

tcf(c_118725,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_106960]) ).

tcf(c_118726,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_105967]) ).

tcf(c_118728,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_95608]) ).

tcf(c_118731,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_117861,c_98014]) ).

tcf(c_118732,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_95414]) ).

tcf(c_118733,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_95286]) ).

tcf(c_118734,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_95041]) ).

tcf(c_118735,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_94695]) ).

tcf(c_118736,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_94594]) ).

tcf(c_118737,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_93822]) ).

tcf(c_118738,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_93551]) ).

tcf(c_118739,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117861,c_79918]) ).

tcf(c_118742,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117861,c_83537]) ).

tcf(c_118743,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117861,c_83534]) ).

tcf(c_118749,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_117861,c_96186]) ).

tcf(c_118756,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_118731,c_79573]) ).

tcf(c_118775,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_84386,c_91937]) ).

tcf(c_118776,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_253,c_118775]) ).

tcf(c_118778,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls)),
    inference(superposition,[status(thm)],[c_574,c_118775]) ).

tcf(c_118779,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min)),
    inference(superposition,[status(thm)],[c_76397,c_118775]) ).

tcf(c_118780,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_118775]) ).

tcf(c_118781,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_118775]) ).

tcf(c_118782,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_76399,c_118775]) ).

tcf(c_118783,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_76401,c_118775]) ).

tcf(c_118784,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m)),
    inference(superposition,[status(thm)],[c_76402,c_118775]) ).

tcf(c_118785,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1)),
    inference(superposition,[status(thm)],[c_76403,c_118775]) ).

tcf(c_118786,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s)),
    inference(superposition,[status(thm)],[c_76404,c_118775]) ).

tcf(c_118787,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t)),
    inference(superposition,[status(thm)],[c_76405,c_118775]) ).

tcf(c_118788,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_118775]) ).

tcf(c_118789,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_118775]) ).

tcf(c_118790,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_118775]) ).

tcf(c_118791,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_118775]) ).

tcf(c_118792,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_118775]) ).

tcf(c_118793,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_118775]) ).

tcf(c_118794,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_118775]) ).

tcf(c_118795,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_118775]) ).

tcf(c_118796,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_118775]) ).

tcf(c_118797,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_118775]) ).

tcf(c_118798,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_77366,c_118775]) ).

tcf(c_118799,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0))),
    inference(superposition,[status(thm)],[c_78024,c_118775]) ).

tcf(c_118800,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t))),
    inference(superposition,[status(thm)],[c_78042,c_118775]) ).

tcf(c_118801,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_118775]) ).

tcf(c_118802,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_118775]) ).

tcf(c_118804,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_118775]) ).

tcf(c_118806,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_118775]) ).

tcf(c_118807,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_118775]) ).

tcf(c_118809,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_118775]) ).

tcf(c_118810,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_118775]) ).

tcf(c_118811,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_118775]) ).

tcf(c_118812,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_118775]) ).

tcf(c_118813,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_118775]) ).

tcf(c_118814,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_118775]) ).

tcf(c_118815,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_118775]) ).

tcf(c_118816,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96714,c_118775]) ).

tcf(c_118817,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_99171,c_118775]) ).

tcf(c_118818,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_118775]) ).

tcf(c_118819,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_118775]) ).

tcf(c_118820,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),
    inference(superposition,[status(thm)],[c_118775,c_76401]) ).

tcf(c_118824,plain,
    ! [X0: $i,X1: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),hAPP_nat_nat(times_times_nat(one_one_nat),X1)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),X1),
    inference(superposition,[status(thm)],[c_118775,c_676]) ).

tcf(c_118826,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_118775,c_805]) ).

tcf(c_118827,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m)),one_one_nat) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m),
    inference(light_normalisation,[status(thm)],[c_118778,c_77414]) ).

tcf(c_118905,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_131,c_46398]) ).

tcf(c_118907,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),hAPP_nat_nat(minus_minus_nat(number_number_of_nat(X1)),number_number_of_nat(X0))) = number_number_of_nat(X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_1353,c_46398]) ).

tcf(c_118908,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1)))
      | ( number_number_of_nat(X0) = number_number_of_nat(X1) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_1259,c_46398]) ).

tcf(c_118909,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_786,c_46398]) ).

tcf(c_118911,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,iPr_def_11),number_number_of_nat(X0))) ),
    inference(superposition,[status(thm)],[c_78547,c_46398]) ).

tcf(c_118912,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_786,c_46398]) ).

tcf(c_118913,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_78282,c_46398]) ).

tcf(c_118914,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_78547,c_46398]) ).

tcf(c_118937,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),X2))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_676,c_46400]) ).

tcf(c_118942,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_82861,c_46400]) ).

tcf(c_118965,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) ),
    inference(superposition,[status(thm)],[c_98914,c_46400]) ).

tcf(c_118966,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))) ),
    inference(superposition,[status(thm)],[c_99040,c_46400]) ).

tcf(c_118967,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))) ),
    inference(superposition,[status(thm)],[c_118775,c_46400]) ).

tcf(c_118968,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),X1)),pls)) ),
    inference(superposition,[status(thm)],[c_46400,c_46112]) ).

tcf(c_118969,plain,
    ! [X0: $i,X1: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(member_int(hAPP_nat_int(power_power_int(X0),X1),d22set(pls))) ),
    inference(superposition,[status(thm)],[c_46400,c_1579]) ).

tcf(c_118970,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_nat_int(power_power_int(X0),X1),hAPP_i1948725293t_bool(ord_less_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46400,c_226]) ).

tcf(c_119002,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83483,c_46410]) ).

tcf(c_119004,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(superposition,[status(thm)],[c_84522,c_46410]) ).

tcf(c_119005,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_84527,c_46410]) ).

tcf(c_119006,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_84528,c_46410]) ).

tcf(c_119011,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_92002,c_46410]) ).

tcf(c_119012,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_98912,c_46410]) ).

tcf(c_119016,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(div_mod_int(X1),X0),hAPP_i1948725293t_bool(ord_less_eq_int,pls)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46410,c_226]) ).

tcf(c_119039,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,sK30(iPr_def_19)),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83483,c_46416]) ).

tcf(c_119041,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),one_one_int)) ),
    inference(superposition,[status(thm)],[c_84522,c_46416]) ).

tcf(c_119042,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,iPr_def_16),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_84527,c_46416]) ).

tcf(c_119043,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,m),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),m)) ),
    inference(superposition,[status(thm)],[c_84528,c_46416]) ).

tcf(c_119048,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_92002,c_46416]) ).

tcf(c_119049,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_98912,c_46416]) ).

tcf(c_119053,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(div_mod_int(X1),X0),cOMBC_int_int_bool(ord_less_int,X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_46416,c_226]) ).

tcf(c_119060,plain,
    hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,one_one_int),pls)),
    inference(forward_subsumption_resolution,[status(thm)],[c_119041,c_114]) ).

tcf(c_119069,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),X0)) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_46106]) ).

tcf(c_119070,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(s,hAPP_int_int(iPr_def_13,s),s))),X0) = pls,
    inference(superposition,[status(thm)],[c_116990,c_46104]) ).

tcf(c_119071,plain,
    hAPP_int_int(minus_minus_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),pls) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_880]) ).

tcf(c_119072,plain,
    hAPP_nat_int(power_power_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),one_one_nat) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_608]) ).

tcf(c_119073,plain,
    hAPP_int_int(plus_plus_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),pls) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_524]) ).

tcf(c_119074,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(s,hAPP_int_int(iPr_def_13,s),s)) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_523]) ).

tcf(c_119075,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(s,hAPP_int_int(iPr_def_13,s),s)) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_347]) ).

tcf(c_119076,plain,
    hAPP_int_int(times_times_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)),one_one_int) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_346]) ).

tcf(c_119077,plain,
    number_number_of_int(sK14(s,hAPP_int_int(iPr_def_13,s),s)) = sK14(s,hAPP_int_int(iPr_def_13,s),s),
    inference(superposition,[status(thm)],[c_116990,c_254]) ).

tcf(c_119096,plain,
    hBOOL(member_int(s,zcong(hAPP_int_int(iPr_def_13,s),s))),
    inference(superposition,[status(thm)],[c_116989,c_226]) ).

tcf(c_119097,plain,
    ( is_int(sK14(hAPP_int_int(iPr_def_13,s),s,s))
    | ~ is_int(s) ),
    inference(superposition,[status(thm)],[c_116989,c_852]) ).

tcf(c_119099,plain,
    is_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),
    inference(forward_subsumption_resolution,[status(thm)],[c_119097,c_72]) ).

tcf(c_119100,plain,
    hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),one_one_nat) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_118797,c_253]) ).

tcf(c_119101,plain,
    number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_119100,c_76401]) ).

tcf(c_119103,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))) ),
    inference(superposition,[status(thm)],[c_119100,c_46400]) ).

tcf(c_119106,plain,
    ! [X0: $i] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_nat_nat(times_times_nat(one_one_nat),X0)) = hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),X0),
    inference(superposition,[status(thm)],[c_119100,c_676]) ).

tcf(c_119108,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    inference(superposition,[status(thm)],[c_119100,c_805]) ).

tcf(c_119112,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_118422]) ).

tcf(c_119113,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_118422]) ).

tcf(c_119114,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_118422]) ).

tcf(c_119115,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_118422]) ).

tcf(c_119117,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_118422]) ).

tcf(c_119118,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_118422]) ).

tcf(c_119120,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_118422]) ).

tcf(c_119121,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_118422]) ).

tcf(c_119122,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_118422]) ).

tcf(c_119123,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_118422]) ).

tcf(c_119124,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_118422]) ).

tcf(c_119125,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_118422]) ).

tcf(c_119126,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_118422]) ).

tcf(c_119127,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_118422]) ).

tcf(c_119128,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_118422]) ).

tcf(c_119129,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_118422]) ).

tcf(c_119130,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_118422]) ).

tcf(c_119131,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_118422]) ).

tcf(c_119132,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_118422]) ).

tcf(c_119133,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_118422]) ).

tcf(c_119134,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_118422]) ).

tcf(c_119135,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_118422]) ).

tcf(c_119136,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_118422]) ).

tcf(c_119137,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_118422]) ).

tcf(c_119138,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_118422]) ).

tcf(c_119139,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_118422]) ).

tcf(c_119140,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_118422]) ).

tcf(c_119141,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_118422]) ).

tcf(c_119142,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_118422]) ).

tcf(c_119143,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_118422]) ).

tcf(c_119144,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_118422]) ).

tcf(c_119145,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_118422]) ).

tcf(c_119146,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_118422]) ).

tcf(c_119147,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_118422]) ).

tcf(c_119148,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_118422]) ).

tcf(c_119149,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_118422]) ).

tcf(c_119150,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_118422]) ).

tcf(c_119151,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_118422]) ).

tcf(c_119152,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_118422]) ).

tcf(c_119153,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_118422]) ).

tcf(c_119154,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_118422]) ).

tcf(c_119155,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_118422]) ).

tcf(c_119156,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_118422]) ).

tcf(c_119157,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_118422]) ).

tcf(c_119158,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_118422]) ).

tcf(c_119159,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_118422]) ).

tcf(c_119160,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_118422]) ).

tcf(c_119161,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_118422]) ).

tcf(c_119162,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_118422]) ).

tcf(c_119163,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_118422]) ).

tcf(c_119164,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_118422]) ).

tcf(c_119165,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_118422]) ).

tcf(c_119166,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_118422]) ).

tcf(c_119167,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_118422]) ).

tcf(c_119168,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_118422]) ).

tcf(c_119169,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_118422]) ).

tcf(c_119170,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_118422]) ).

tcf(c_119171,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_118422]) ).

tcf(c_119172,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_118422]) ).

tcf(c_119173,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_118422]) ).

tcf(c_119174,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_118422]) ).

tcf(c_119175,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_118422]) ).

tcf(c_119176,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_118422]) ).

tcf(c_119177,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_118422]) ).

tcf(c_119178,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_118422]) ).

tcf(c_119179,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_118422]) ).

tcf(c_119180,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_118422]) ).

tcf(c_119181,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_118422]) ).

tcf(c_119182,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_118422]) ).

tcf(c_119183,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_118422]) ).

tcf(c_119184,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_118422]) ).

tcf(c_119185,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_118422]) ).

tcf(c_119186,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_118422]) ).

tcf(c_119187,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_118422]) ).

tcf(c_119188,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_118422]) ).

tcf(c_119189,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_118422]) ).

tcf(c_119190,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_118422]) ).

tcf(c_119191,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_118422]) ).

tcf(c_119192,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_118422]) ).

tcf(c_119193,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_118422]) ).

tcf(c_119196,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_92656]) ).

tcf(c_119197,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_118422,c_255]) ).

tcf(c_119199,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118422,c_256]) ).

tcf(c_119202,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_118422,c_83532]) ).

tcf(c_119203,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_118422,c_83524]) ).

tcf(c_119204,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_118422]) ).

tcf(c_119205,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_117980]) ).

tcf(c_119206,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_117134]) ).

tcf(c_119207,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_115780]) ).

tcf(c_119208,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_115349]) ).

tcf(c_119209,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_114908]) ).

tcf(c_119210,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_114369]) ).

tcf(c_119211,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_113744]) ).

tcf(c_119212,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_113419]) ).

tcf(c_119213,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_112967]) ).

tcf(c_119214,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_112089]) ).

tcf(c_119215,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_111767]) ).

tcf(c_119216,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_111405]) ).

tcf(c_119217,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_111079]) ).

tcf(c_119218,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_110591]) ).

tcf(c_119219,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_109784]) ).

tcf(c_119220,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_109567]) ).

tcf(c_119221,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_108992]) ).

tcf(c_119222,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_107183]) ).

tcf(c_119226,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_106960]) ).

tcf(c_119227,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_105967]) ).

tcf(c_119229,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_95608]) ).

tcf(c_119232,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_118422,c_98014]) ).

tcf(c_119233,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_95414]) ).

tcf(c_119234,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_95286]) ).

tcf(c_119235,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_95041]) ).

tcf(c_119236,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_94695]) ).

tcf(c_119237,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_94594]) ).

tcf(c_119238,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_93822]) ).

tcf(c_119239,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_93551]) ).

tcf(c_119240,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118422,c_79918]) ).

tcf(c_119243,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118422,c_83537]) ).

tcf(c_119244,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118422,c_83534]) ).

tcf(c_119250,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118422,c_96186]) ).

tcf(c_119251,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119117,c_59636]) ).

tcf(c_119252,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119112,c_79190]) ).

tcf(c_119253,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119240,c_76415]) ).

tcf(c_119254,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119120,c_76855,c_93903]) ).

tcf(c_119258,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_119232,c_79573]) ).

tcf(c_119550,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_92656]) ).

tcf(c_119551,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_118300,c_255]) ).

tcf(c_119553,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118300,c_256]) ).

tcf(c_119556,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_118300,c_83532]) ).

tcf(c_119557,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_118300,c_83524]) ).

tcf(c_119558,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_118422]) ).

tcf(c_119559,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_117980]) ).

tcf(c_119560,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_117134]) ).

tcf(c_119561,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_115780]) ).

tcf(c_119562,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_115349]) ).

tcf(c_119563,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_114908]) ).

tcf(c_119564,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_114369]) ).

tcf(c_119565,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_113744]) ).

tcf(c_119566,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_113419]) ).

tcf(c_119567,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_112967]) ).

tcf(c_119568,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_112089]) ).

tcf(c_119569,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_111767]) ).

tcf(c_119570,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_111405]) ).

tcf(c_119571,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_111079]) ).

tcf(c_119572,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_110591]) ).

tcf(c_119573,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_109784]) ).

tcf(c_119574,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_109567]) ).

tcf(c_119575,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_108992]) ).

tcf(c_119576,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_107183]) ).

tcf(c_119580,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_106960]) ).

tcf(c_119581,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_105967]) ).

tcf(c_119583,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_95608]) ).

tcf(c_119586,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_118300,c_98014]) ).

tcf(c_119587,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_95414]) ).

tcf(c_119588,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_95286]) ).

tcf(c_119589,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_95041]) ).

tcf(c_119590,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_94695]) ).

tcf(c_119591,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_94594]) ).

tcf(c_119592,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_93822]) ).

tcf(c_119593,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_93551]) ).

tcf(c_119594,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118300,c_79918]) ).

tcf(c_119597,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118300,c_83537]) ).

tcf(c_119598,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118300,c_83534]) ).

tcf(c_119604,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_118300,c_96186]) ).

tcf(c_119611,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_119586,c_79573]) ).

tcf(c_119727,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_119253]) ).

tcf(c_119728,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_119253]) ).

tcf(c_119729,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_119253]) ).

tcf(c_119730,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_119253]) ).

tcf(c_119732,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_119253]) ).

tcf(c_119733,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_119253]) ).

tcf(c_119735,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_119253]) ).

tcf(c_119736,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_119253]) ).

tcf(c_119737,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_119253]) ).

tcf(c_119738,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_119253]) ).

tcf(c_119739,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_119253]) ).

tcf(c_119740,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_119253]) ).

tcf(c_119741,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_119253]) ).

tcf(c_119742,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_119253]) ).

tcf(c_119743,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_119253]) ).

tcf(c_119744,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_119253]) ).

tcf(c_119745,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_119253]) ).

tcf(c_119746,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_119253]) ).

tcf(c_119747,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_119253]) ).

tcf(c_119748,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_119253]) ).

tcf(c_119749,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_119253]) ).

tcf(c_119750,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_119253]) ).

tcf(c_119751,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_119253]) ).

tcf(c_119752,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_119253]) ).

tcf(c_119753,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_119253]) ).

tcf(c_119754,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_119253]) ).

tcf(c_119755,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_119253]) ).

tcf(c_119756,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_119253]) ).

tcf(c_119757,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_119253]) ).

tcf(c_119758,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_119253]) ).

tcf(c_119759,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_119253]) ).

tcf(c_119760,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_119253]) ).

tcf(c_119761,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_119253]) ).

tcf(c_119762,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_119253]) ).

tcf(c_119763,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_119253]) ).

tcf(c_119764,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_119253]) ).

tcf(c_119765,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_119253]) ).

tcf(c_119766,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_119253]) ).

tcf(c_119767,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_119253]) ).

tcf(c_119768,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_119253]) ).

tcf(c_119769,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_119253]) ).

tcf(c_119770,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_119253]) ).

tcf(c_119771,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_119253]) ).

tcf(c_119772,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_119253]) ).

tcf(c_119773,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_119253]) ).

tcf(c_119774,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_119253]) ).

tcf(c_119775,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_119253]) ).

tcf(c_119776,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_119253]) ).

tcf(c_119777,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_119253]) ).

tcf(c_119778,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_119253]) ).

tcf(c_119779,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_119253]) ).

tcf(c_119780,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_119253]) ).

tcf(c_119781,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_119253]) ).

tcf(c_119782,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_119253]) ).

tcf(c_119783,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_119253]) ).

tcf(c_119784,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_119253]) ).

tcf(c_119785,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_119253]) ).

tcf(c_119786,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_119253]) ).

tcf(c_119787,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_119253]) ).

tcf(c_119788,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_119253]) ).

tcf(c_119789,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_119253]) ).

tcf(c_119790,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_119253]) ).

tcf(c_119791,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_119253]) ).

tcf(c_119792,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_119253]) ).

tcf(c_119793,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_119253]) ).

tcf(c_119794,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_119253]) ).

tcf(c_119795,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_119253]) ).

tcf(c_119796,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_119253]) ).

tcf(c_119797,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_119253]) ).

tcf(c_119798,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_119253]) ).

tcf(c_119799,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_119253]) ).

tcf(c_119800,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_119253]) ).

tcf(c_119801,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_119253]) ).

tcf(c_119802,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_119253]) ).

tcf(c_119803,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_119253]) ).

tcf(c_119804,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_119253]) ).

tcf(c_119805,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_119253]) ).

tcf(c_119806,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_119253]) ).

tcf(c_119807,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_119253]) ).

tcf(c_119808,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_119253]) ).

tcf(c_119809,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_119253]) ).

tcf(c_119810,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_119253]) ).

tcf(c_119813,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_92656]) ).

tcf(c_119814,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_119253,c_255]) ).

tcf(c_119816,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119253,c_256]) ).

tcf(c_119819,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_119253,c_83532]) ).

tcf(c_119820,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_119253,c_83524]) ).

tcf(c_119821,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_119253]) ).

tcf(c_119822,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_118422]) ).

tcf(c_119823,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_117980]) ).

tcf(c_119824,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_117134]) ).

tcf(c_119825,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_115780]) ).

tcf(c_119826,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_115349]) ).

tcf(c_119827,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_114908]) ).

tcf(c_119828,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_114369]) ).

tcf(c_119829,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_113744]) ).

tcf(c_119830,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_113419]) ).

tcf(c_119831,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_112967]) ).

tcf(c_119832,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_112089]) ).

tcf(c_119833,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_111767]) ).

tcf(c_119834,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_111405]) ).

tcf(c_119835,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_111079]) ).

tcf(c_119836,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_110591]) ).

tcf(c_119837,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_109784]) ).

tcf(c_119838,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_109567]) ).

tcf(c_119839,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_108992]) ).

tcf(c_119840,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_107183]) ).

tcf(c_119844,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_106960]) ).

tcf(c_119845,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_105967]) ).

tcf(c_119847,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_95608]) ).

tcf(c_119850,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_119253,c_98014]) ).

tcf(c_119851,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_95414]) ).

tcf(c_119852,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_95286]) ).

tcf(c_119853,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_95041]) ).

tcf(c_119854,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_94695]) ).

tcf(c_119855,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_94594]) ).

tcf(c_119856,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_93822]) ).

tcf(c_119857,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_93551]) ).

tcf(c_119858,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119253,c_79918]) ).

tcf(c_119861,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119253,c_83537]) ).

tcf(c_119862,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119253,c_83534]) ).

tcf(c_119868,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119253,c_96186]) ).

tcf(c_119869,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119732,c_59636]) ).

tcf(c_119870,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119727,c_79190]) ).

tcf(c_119871,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119858,c_76415]) ).

tcf(c_119872,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_119735,c_76855,c_93903]) ).

tcf(c_119876,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_119850,c_79573]) ).

tcf(c_120121,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_92656]) ).

tcf(c_120122,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_119128,c_255]) ).

tcf(c_120124,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119128,c_256]) ).

tcf(c_120127,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_119128,c_83532]) ).

tcf(c_120128,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_119128,c_83524]) ).

tcf(c_120129,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_119253]) ).

tcf(c_120130,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_118422]) ).

tcf(c_120131,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_117980]) ).

tcf(c_120132,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_117134]) ).

tcf(c_120133,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_115780]) ).

tcf(c_120134,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_115349]) ).

tcf(c_120135,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_114908]) ).

tcf(c_120136,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_114369]) ).

tcf(c_120137,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_113744]) ).

tcf(c_120138,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_113419]) ).

tcf(c_120139,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_112967]) ).

tcf(c_120140,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_112089]) ).

tcf(c_120141,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_111767]) ).

tcf(c_120142,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_111405]) ).

tcf(c_120143,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_111079]) ).

tcf(c_120144,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_110591]) ).

tcf(c_120145,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_109784]) ).

tcf(c_120146,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_109567]) ).

tcf(c_120147,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_108992]) ).

tcf(c_120148,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_107183]) ).

tcf(c_120152,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_106960]) ).

tcf(c_120153,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_105967]) ).

tcf(c_120155,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_95608]) ).

tcf(c_120158,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_119128,c_98014]) ).

tcf(c_120159,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_95414]) ).

tcf(c_120160,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_95286]) ).

tcf(c_120161,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_95041]) ).

tcf(c_120162,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_94695]) ).

tcf(c_120163,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_94594]) ).

tcf(c_120164,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_93822]) ).

tcf(c_120165,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_93551]) ).

tcf(c_120166,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119128,c_79918]) ).

tcf(c_120169,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119128,c_83537]) ).

tcf(c_120170,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119128,c_83534]) ).

tcf(c_120176,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119128,c_96186]) ).

tcf(c_120183,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_120158,c_79573]) ).

tcf(c_120203,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_119871]) ).

tcf(c_120204,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_119871]) ).

tcf(c_120205,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_119871]) ).

tcf(c_120206,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_119871]) ).

tcf(c_120208,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_119871]) ).

tcf(c_120209,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_119871]) ).

tcf(c_120211,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_119871]) ).

tcf(c_120212,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_119871]) ).

tcf(c_120213,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_119871]) ).

tcf(c_120214,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_119871]) ).

tcf(c_120215,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_119871]) ).

tcf(c_120216,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_119871]) ).

tcf(c_120217,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_119871]) ).

tcf(c_120218,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_119871]) ).

tcf(c_120219,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_119871]) ).

tcf(c_120220,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_119871]) ).

tcf(c_120221,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_119871]) ).

tcf(c_120222,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_119871]) ).

tcf(c_120223,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_119871]) ).

tcf(c_120224,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_119871]) ).

tcf(c_120225,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_119871]) ).

tcf(c_120226,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_119871]) ).

tcf(c_120227,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_119871]) ).

tcf(c_120228,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_119871]) ).

tcf(c_120229,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_119871]) ).

tcf(c_120230,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_119871]) ).

tcf(c_120231,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_119871]) ).

tcf(c_120232,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_119871]) ).

tcf(c_120233,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_119871]) ).

tcf(c_120234,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_119871]) ).

tcf(c_120235,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_119871]) ).

tcf(c_120236,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_119871]) ).

tcf(c_120237,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_119871]) ).

tcf(c_120238,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_119871]) ).

tcf(c_120239,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_119871]) ).

tcf(c_120240,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_119871]) ).

tcf(c_120241,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_119871]) ).

tcf(c_120242,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_119871]) ).

tcf(c_120243,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_119871]) ).

tcf(c_120244,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_119871]) ).

tcf(c_120245,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_119871]) ).

tcf(c_120246,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_119871]) ).

tcf(c_120247,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_119871]) ).

tcf(c_120248,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_119871]) ).

tcf(c_120249,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_119871]) ).

tcf(c_120250,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_119871]) ).

tcf(c_120251,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_119871]) ).

tcf(c_120252,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_119871]) ).

tcf(c_120253,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_119871]) ).

tcf(c_120254,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_119871]) ).

tcf(c_120255,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_119871]) ).

tcf(c_120256,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_119871]) ).

tcf(c_120257,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_119871]) ).

tcf(c_120258,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_119871]) ).

tcf(c_120259,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_119871]) ).

tcf(c_120260,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_119871]) ).

tcf(c_120261,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_119871]) ).

tcf(c_120262,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_119871]) ).

tcf(c_120263,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_119871]) ).

tcf(c_120264,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_119871]) ).

tcf(c_120265,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_119871]) ).

tcf(c_120266,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_119871]) ).

tcf(c_120267,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_119871]) ).

tcf(c_120268,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_119871]) ).

tcf(c_120269,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_119871]) ).

tcf(c_120270,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_119871]) ).

tcf(c_120271,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_119871]) ).

tcf(c_120272,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_119871]) ).

tcf(c_120273,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_119871]) ).

tcf(c_120274,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_119871]) ).

tcf(c_120275,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_119871]) ).

tcf(c_120276,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_119871]) ).

tcf(c_120277,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_119871]) ).

tcf(c_120278,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_119871]) ).

tcf(c_120279,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_119871]) ).

tcf(c_120280,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_119871]) ).

tcf(c_120281,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_119871]) ).

tcf(c_120282,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_119871]) ).

tcf(c_120283,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_119871]) ).

tcf(c_120284,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_119871]) ).

tcf(c_120285,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_119871]) ).

tcf(c_120286,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_119871]) ).

tcf(c_120287,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_119871]) ).

tcf(c_120288,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_119871]) ).

tcf(c_120291,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_92656]) ).

tcf(c_120292,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_119871,c_255]) ).

tcf(c_120294,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119871,c_256]) ).

tcf(c_120297,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_119871,c_83532]) ).

tcf(c_120298,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_119871,c_83524]) ).

tcf(c_120299,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_119871]) ).

tcf(c_120300,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_119253]) ).

tcf(c_120301,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_118422]) ).

tcf(c_120302,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_117980]) ).

tcf(c_120303,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_117134]) ).

tcf(c_120304,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_115780]) ).

tcf(c_120305,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_115349]) ).

tcf(c_120306,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_114908]) ).

tcf(c_120307,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_114369]) ).

tcf(c_120308,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_113744]) ).

tcf(c_120309,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_113419]) ).

tcf(c_120310,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_112967]) ).

tcf(c_120311,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_112089]) ).

tcf(c_120312,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_111767]) ).

tcf(c_120313,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_111405]) ).

tcf(c_120314,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_111079]) ).

tcf(c_120315,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_110591]) ).

tcf(c_120316,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_109784]) ).

tcf(c_120317,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_109567]) ).

tcf(c_120318,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_108992]) ).

tcf(c_120319,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_107183]) ).

tcf(c_120323,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_106960]) ).

tcf(c_120324,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_105967]) ).

tcf(c_120326,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_95608]) ).

tcf(c_120329,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_119871,c_98014]) ).

tcf(c_120330,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_95414]) ).

tcf(c_120331,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_95286]) ).

tcf(c_120332,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_95041]) ).

tcf(c_120333,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_94695]) ).

tcf(c_120334,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_94594]) ).

tcf(c_120335,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_93822]) ).

tcf(c_120336,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_93551]) ).

tcf(c_120337,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119871,c_79918]) ).

tcf(c_120340,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119871,c_83537]) ).

tcf(c_120341,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119871,c_83534]) ).

tcf(c_120347,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119871,c_96186]) ).

tcf(c_120348,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120208,c_59636]) ).

tcf(c_120349,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120203,c_79190]) ).

tcf(c_120350,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120337,c_76415]) ).

tcf(c_120351,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120211,c_76855,c_93903]) ).

tcf(c_120355,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_120329,c_79573]) ).

tcf(c_120647,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_92656]) ).

tcf(c_120648,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_119743,c_255]) ).

tcf(c_120650,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119743,c_256]) ).

tcf(c_120653,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_119743,c_83532]) ).

tcf(c_120654,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_119743,c_83524]) ).

tcf(c_120655,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_119871]) ).

tcf(c_120656,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_119253]) ).

tcf(c_120657,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_118422]) ).

tcf(c_120658,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_117980]) ).

tcf(c_120659,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_117134]) ).

tcf(c_120660,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_115780]) ).

tcf(c_120661,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_115349]) ).

tcf(c_120662,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_114908]) ).

tcf(c_120663,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_114369]) ).

tcf(c_120664,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_113744]) ).

tcf(c_120665,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_113419]) ).

tcf(c_120666,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_112967]) ).

tcf(c_120667,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_112089]) ).

tcf(c_120668,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_111767]) ).

tcf(c_120669,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_111405]) ).

tcf(c_120670,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_111079]) ).

tcf(c_120671,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_110591]) ).

tcf(c_120672,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_109784]) ).

tcf(c_120673,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_109567]) ).

tcf(c_120674,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_108992]) ).

tcf(c_120675,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_107183]) ).

tcf(c_120679,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_106960]) ).

tcf(c_120680,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_105967]) ).

tcf(c_120682,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_95608]) ).

tcf(c_120685,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_119743,c_98014]) ).

tcf(c_120686,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_95414]) ).

tcf(c_120687,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_95286]) ).

tcf(c_120688,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_95041]) ).

tcf(c_120689,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_94695]) ).

tcf(c_120690,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_94594]) ).

tcf(c_120691,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_93822]) ).

tcf(c_120692,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_93551]) ).

tcf(c_120693,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119743,c_79918]) ).

tcf(c_120696,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119743,c_83537]) ).

tcf(c_120697,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119743,c_83534]) ).

tcf(c_120703,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_119743,c_96186]) ).

tcf(c_120710,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_120685,c_79573]) ).

tcf(c_120807,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_120350]) ).

tcf(c_120808,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_120350]) ).

tcf(c_120809,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_120350]) ).

tcf(c_120810,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_120350]) ).

tcf(c_120812,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_120350]) ).

tcf(c_120813,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_120350]) ).

tcf(c_120815,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_120350]) ).

tcf(c_120816,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_120350]) ).

tcf(c_120817,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_120350]) ).

tcf(c_120818,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_120350]) ).

tcf(c_120819,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_120350]) ).

tcf(c_120820,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_120350]) ).

tcf(c_120821,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_120350]) ).

tcf(c_120822,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_120350]) ).

tcf(c_120823,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_120350]) ).

tcf(c_120824,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_120350]) ).

tcf(c_120825,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_120350]) ).

tcf(c_120826,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_120350]) ).

tcf(c_120827,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_120350]) ).

tcf(c_120828,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_120350]) ).

tcf(c_120829,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_120350]) ).

tcf(c_120830,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_120350]) ).

tcf(c_120831,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_120350]) ).

tcf(c_120832,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_120350]) ).

tcf(c_120833,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_120350]) ).

tcf(c_120834,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_120350]) ).

tcf(c_120835,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_120350]) ).

tcf(c_120836,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_120350]) ).

tcf(c_120837,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_120350]) ).

tcf(c_120838,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_120350]) ).

tcf(c_120839,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_120350]) ).

tcf(c_120840,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_120350]) ).

tcf(c_120841,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_120350]) ).

tcf(c_120842,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_120350]) ).

tcf(c_120843,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_120350]) ).

tcf(c_120844,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_120350]) ).

tcf(c_120845,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_120350]) ).

tcf(c_120846,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_120350]) ).

tcf(c_120847,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_120350]) ).

tcf(c_120848,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_120350]) ).

tcf(c_120849,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_120350]) ).

tcf(c_120850,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_120350]) ).

tcf(c_120851,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_120350]) ).

tcf(c_120852,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_120350]) ).

tcf(c_120853,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_120350]) ).

tcf(c_120854,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_120350]) ).

tcf(c_120855,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_120350]) ).

tcf(c_120856,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_120350]) ).

tcf(c_120857,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_120350]) ).

tcf(c_120858,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_120350]) ).

tcf(c_120859,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_120350]) ).

tcf(c_120860,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_120350]) ).

tcf(c_120861,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_120350]) ).

tcf(c_120862,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_120350]) ).

tcf(c_120863,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_120350]) ).

tcf(c_120864,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_120350]) ).

tcf(c_120865,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_120350]) ).

tcf(c_120866,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_120350]) ).

tcf(c_120867,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_120350]) ).

tcf(c_120868,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_120350]) ).

tcf(c_120869,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_120350]) ).

tcf(c_120870,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_120350]) ).

tcf(c_120871,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_120350]) ).

tcf(c_120872,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_120350]) ).

tcf(c_120873,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_120350]) ).

tcf(c_120874,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_120350]) ).

tcf(c_120875,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_120350]) ).

tcf(c_120876,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_120350]) ).

tcf(c_120877,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_120350]) ).

tcf(c_120878,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_120350]) ).

tcf(c_120879,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_120350]) ).

tcf(c_120880,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_120350]) ).

tcf(c_120881,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_120350]) ).

tcf(c_120882,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_120350]) ).

tcf(c_120883,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_120350]) ).

tcf(c_120884,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_120350]) ).

tcf(c_120885,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_120350]) ).

tcf(c_120886,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_120350]) ).

tcf(c_120887,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_120350]) ).

tcf(c_120888,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_120350]) ).

tcf(c_120889,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_120350]) ).

tcf(c_120890,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_120350]) ).

tcf(c_120891,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_120350]) ).

tcf(c_120892,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_120350]) ).

tcf(c_120893,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_120350]) ).

tcf(c_120894,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_120350]) ).

tcf(c_120897,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_92656]) ).

tcf(c_120898,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_120350,c_255]) ).

tcf(c_120900,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120350,c_256]) ).

tcf(c_120903,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_120350,c_83532]) ).

tcf(c_120904,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_120350,c_83524]) ).

tcf(c_120905,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_120350]) ).

tcf(c_120906,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_119871]) ).

tcf(c_120907,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_119253]) ).

tcf(c_120908,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_118422]) ).

tcf(c_120909,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_117980]) ).

tcf(c_120910,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_117134]) ).

tcf(c_120911,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_115780]) ).

tcf(c_120912,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_115349]) ).

tcf(c_120913,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_114908]) ).

tcf(c_120914,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_114369]) ).

tcf(c_120915,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_113744]) ).

tcf(c_120916,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_113419]) ).

tcf(c_120917,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_112967]) ).

tcf(c_120918,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_112089]) ).

tcf(c_120919,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_111767]) ).

tcf(c_120920,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_111405]) ).

tcf(c_120921,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_111079]) ).

tcf(c_120922,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_110591]) ).

tcf(c_120923,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_109784]) ).

tcf(c_120924,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_109567]) ).

tcf(c_120925,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_108992]) ).

tcf(c_120926,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_107183]) ).

tcf(c_120930,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_106960]) ).

tcf(c_120931,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_105967]) ).

tcf(c_120933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_95608]) ).

tcf(c_120936,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_120350,c_98014]) ).

tcf(c_120937,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_95414]) ).

tcf(c_120938,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_95286]) ).

tcf(c_120939,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_95041]) ).

tcf(c_120940,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_94695]) ).

tcf(c_120941,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_94594]) ).

tcf(c_120942,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_93822]) ).

tcf(c_120943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_93551]) ).

tcf(c_120944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120350,c_79918]) ).

tcf(c_120947,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120350,c_83537]) ).

tcf(c_120948,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120350,c_83534]) ).

tcf(c_120954,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120350,c_96186]) ).

tcf(c_120955,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120812,c_59636]) ).

tcf(c_120956,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120807,c_79190]) ).

tcf(c_120957,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120944,c_76415]) ).

tcf(c_120958,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_120815,c_76855,c_93903]) ).

tcf(c_120962,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_120936,c_79573]) ).

tcf(c_121392,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),
    inference(demodulation,[status(thm)],[c_84387,c_91937]) ).

tcf(c_121393,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(superposition,[status(thm)],[c_253,c_121392]) ).

tcf(c_121395,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),pls)),
    inference(superposition,[status(thm)],[c_574,c_121392]) ).

tcf(c_121396,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),min)),
    inference(superposition,[status(thm)],[c_76397,c_121392]) ).

tcf(c_121397,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),one_one_int)),
    inference(superposition,[status(thm)],[c_76393,c_121392]) ).

tcf(c_121398,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),undefined_int(int))),
    inference(superposition,[status(thm)],[c_76395,c_121392]) ).

tcf(c_121399,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),twoSqu1241645765sum2sq(X0))),
    inference(superposition,[status(thm)],[c_76399,c_121392]) ).

tcf(c_121400,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_nat_int(X0,X1))),
    inference(superposition,[status(thm)],[c_76401,c_121392]) ).

tcf(c_121401,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),m)),
    inference(superposition,[status(thm)],[c_76402,c_121392]) ).

tcf(c_121402,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s1)),
    inference(superposition,[status(thm)],[c_76403,c_121392]) ).

tcf(c_121403,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),s)),
    inference(superposition,[status(thm)],[c_76404,c_121392]) ).

tcf(c_121404,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),t)),
    inference(superposition,[status(thm)],[c_76405,c_121392]) ).

tcf(c_121405,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK9)),
    inference(superposition,[status(thm)],[c_76406,c_121392]) ).

tcf(c_121406,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK10)),
    inference(superposition,[status(thm)],[c_76407,c_121392]) ).

tcf(c_121407,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK11)),
    inference(superposition,[status(thm)],[c_76408,c_121392]) ).

tcf(c_121408,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK13)),
    inference(superposition,[status(thm)],[c_76409,c_121392]) ).

tcf(c_121409,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_14)),
    inference(superposition,[status(thm)],[c_76410,c_121392]) ).

tcf(c_121410,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_15)),
    inference(superposition,[status(thm)],[c_76411,c_121392]) ).

tcf(c_121411,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_16)),
    inference(superposition,[status(thm)],[c_76412,c_121392]) ).

tcf(c_121412,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_17)),
    inference(superposition,[status(thm)],[c_76413,c_121392]) ).

tcf(c_121413,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),iPr_def_18)),
    inference(superposition,[status(thm)],[c_76414,c_121392]) ).

tcf(c_121414,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),
    inference(superposition,[status(thm)],[c_76415,c_121392]) ).

tcf(c_121415,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_13,X0))),
    inference(superposition,[status(thm)],[c_77366,c_121392]) ).

tcf(c_121416,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(iPr_def_12,X0))),
    inference(superposition,[status(thm)],[c_78024,c_121392]) ).

tcf(c_121417,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,t))),
    inference(superposition,[status(thm)],[c_78042,c_121392]) ).

tcf(c_121418,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK27(X0,one_one_int))),
    inference(superposition,[status(thm)],[c_78056,c_121392]) ).

tcf(c_121419,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK26(iPr_def_14))),
    inference(superposition,[status(thm)],[c_78203,c_121392]) ).

tcf(c_121421,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79414,c_121392]) ).

tcf(c_121423,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_79437,c_121392]) ).

tcf(c_121424,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_79918,c_121392]) ).

tcf(c_121426,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80664,c_121392]) ).

tcf(c_121427,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_80677,c_121392]) ).

tcf(c_121428,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m))),
    inference(superposition,[status(thm)],[c_80692,c_121392]) ).

tcf(c_121429,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_80705,c_121392]) ).

tcf(c_121430,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88502,c_121392]) ).

tcf(c_121431,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88521,c_121392]) ).

tcf(c_121432,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))),
    inference(superposition,[status(thm)],[c_88558,c_121392]) ).

tcf(c_121433,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_96714,c_121392]) ).

tcf(c_121434,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)))),
    inference(superposition,[status(thm)],[c_99171,c_121392]) ).

tcf(c_121435,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_100498,c_121392]) ).

tcf(c_121436,plain,
    ! [X0: $i] : hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))),
    inference(superposition,[status(thm)],[c_103848,c_121392]) ).

tcf(c_121438,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))),pls)) ),
    inference(superposition,[status(thm)],[c_121392,c_45986]) ).

tcf(c_121439,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),pls),X1)) ),
    inference(superposition,[status(thm)],[c_121392,c_897]) ).

tcf(c_121440,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X1))))) ),
    inference(superposition,[status(thm)],[c_121392,c_896]) ).

tcf(c_121441,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m)),pls) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),m),
    inference(light_normalisation,[status(thm)],[c_121395,c_77414]) ).

tcf(c_121527,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | ( hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(X1),number_number_of_nat(X2))) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_675,c_46446]) ).

tcf(c_121530,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ( hAPP_nat_real(power_power_real(X0),zero_zero_nat) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_786,c_46446]) ).

tcf(c_121531,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls))
      | ( hAPP_nat_real(power_power_real(X0),zero_zero_nat) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_78282,c_46446]) ).

tcf(c_121532,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),pls))
      | ( hAPP_nat_real(power_power_real(X0),iPr_def_11) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_78547,c_46446]) ).

tcf(c_121535,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls))
    | ( one_one_real != zero_zero_real ) ),
    inference(light_normalisation,[status(thm)],[c_121531,c_782]) ).

tcf(c_121536,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ( one_one_real != zero_zero_real ) ),
    inference(light_normalisation,[status(thm)],[c_121530,c_782]) ).

tcf(c_121545,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),hAPP_nat_nat(times_times_nat(X1),number_number_of_nat(X2))) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_674,c_46448]) ).

tcf(c_121548,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_786,c_46448]) ).

tcf(c_121549,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_78282,c_46448]) ).

tcf(c_121550,plain,
    ! [X0: $i] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,iPr_def_14),pls))
      | ( hAPP_nat_nat(power_power_nat(X0),iPr_def_11) != zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_78547,c_46448]) ).

tcf(c_121553,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls))
    | ( one_one_nat != zero_zero_nat ) ),
    inference(light_normalisation,[status(thm)],[c_121549,c_1223]) ).

tcf(c_121554,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
    | ( one_one_nat != zero_zero_nat ) ),
    inference(light_normalisation,[status(thm)],[c_121548,c_1223]) ).

tcf(c_121563,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X0),iPr_def_11)),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_82316,c_46504]) ).

tcf(c_121565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),X0))),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1308,c_46504]) ).

tcf(c_121566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X2),X1))),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_218,c_46504]) ).

tcf(c_121569,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1413,c_46504]) ).

tcf(c_121571,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1336,c_46504]) ).

tcf(c_121573,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X1),X0)),sK18(hAPP_nat_nat(times_times_nat(X1),X0),zero_zero_nat)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46504,c_1376]) ).

tcf(c_121574,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46504,c_1332]) ).

tcf(c_121575,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X1),X0) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46504,c_1329]) ).

tcf(c_121630,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2))),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_1308,c_46506]) ).

tcf(c_121631,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X2))),zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_218,c_46506]) ).

tcf(c_121638,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),sK18(hAPP_nat_nat(times_times_nat(X0),X1),zero_zero_nat)) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46506,c_1376]) ).

tcf(c_121639,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46506,c_1332]) ).

tcf(c_121640,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(times_times_nat(X0),X1) = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46506,c_1329]) ).

tcf(c_121654,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),X0)) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_46106]) ).

tcf(c_121655,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,s),s,s))),X0) = pls,
    inference(superposition,[status(thm)],[c_119099,c_46104]) ).

tcf(c_121656,plain,
    hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),pls) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_880]) ).

tcf(c_121657,plain,
    hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_608]) ).

tcf(c_121658,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),pls) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_524]) ).

tcf(c_121659,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,s),s,s)) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_523]) ).

tcf(c_121660,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,s),s,s)) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_347]) ).

tcf(c_121661,plain,
    hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)),one_one_int) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_346]) ).

tcf(c_121662,plain,
    number_number_of_int(sK14(hAPP_int_int(iPr_def_13,s),s,s)) = sK14(hAPP_int_int(iPr_def_13,s),s,s),
    inference(superposition,[status(thm)],[c_119099,c_254]) ).

tcf(c_121673,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(t,hAPP_int_int(times_times_int(t),X0)),t)),
    inference(superposition,[status(thm)],[c_253,c_78308]) ).

tcf(c_121675,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(t,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),t))),t)),
    inference(superposition,[status(thm)],[c_252,c_78308]) ).

tcf(c_121676,plain,
    hBOOL(hAPP_int_bool(zcong(t,pls),t)),
    inference(superposition,[status(thm)],[c_1004,c_78308]) ).

tcf(c_121677,plain,
    hBOOL(hAPP_int_bool(zcong(t,hAPP_int_int(plus_plus_int(t),t)),t)),
    inference(superposition,[status(thm)],[c_79150,c_78308]) ).

tcf(c_121678,plain,
    hBOOL(hAPP_int_bool(zcong(t,hAPP_int_int(iPr_def_13,t)),t)),
    inference(superposition,[status(thm)],[c_59637,c_78308]) ).

tcf(c_121679,plain,
    ! [X0: $i] : hBOOL(member_int(t,zcong(t,hAPP_int_int(times_times_int(X0),t)))),
    inference(superposition,[status(thm)],[c_78308,c_226]) ).

tcf(c_121680,plain,
    ! [X0: $i] :
      ( is_int(sK14(t,hAPP_int_int(times_times_int(X0),t),t))
      | ~ is_int(hAPP_int_int(times_times_int(X0),t)) ),
    inference(superposition,[status(thm)],[c_78308,c_852]) ).

tcf(c_121704,plain,
    hBOOL(member_int(t,zcong(t,hAPP_int_int(iPr_def_13,t)))),
    inference(superposition,[status(thm)],[c_121678,c_226]) ).

tcf(c_121705,plain,
    ( is_int(sK14(t,hAPP_int_int(iPr_def_13,t),t))
    | ~ is_int(hAPP_int_int(iPr_def_13,t)) ),
    inference(superposition,[status(thm)],[c_121678,c_852]) ).

tcf(c_121706,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,t),t),t)),
    inference(superposition,[status(thm)],[c_121678,c_814]) ).

tcf(c_121707,plain,
    is_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),
    inference(forward_subsumption_resolution,[status(thm)],[c_121705,c_77054]) ).

tcf(c_121708,plain,
    hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls) = hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),
    inference(demodulation,[status(thm)],[c_121414,c_253]) ).

tcf(c_121710,plain,
    ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),pls)) ),
    inference(superposition,[status(thm)],[c_121708,c_45986]) ).

tcf(c_121711,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))
      | ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),pls),X0)) ),
    inference(superposition,[status(thm)],[c_121708,c_897]) ).

tcf(c_121712,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))) ),
    inference(superposition,[status(thm)],[c_121708,c_896]) ).

tcf(c_121722,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_92656]) ).

tcf(c_121723,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_120219,c_255]) ).

tcf(c_121725,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120219,c_256]) ).

tcf(c_121728,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_120219,c_83532]) ).

tcf(c_121729,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_120219,c_83524]) ).

tcf(c_121730,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_120350]) ).

tcf(c_121731,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_119871]) ).

tcf(c_121732,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_119253]) ).

tcf(c_121733,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_118422]) ).

tcf(c_121734,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_117980]) ).

tcf(c_121735,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_117134]) ).

tcf(c_121736,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_115780]) ).

tcf(c_121737,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_115349]) ).

tcf(c_121738,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_114908]) ).

tcf(c_121739,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_114369]) ).

tcf(c_121740,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_113744]) ).

tcf(c_121741,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_113419]) ).

tcf(c_121742,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_112967]) ).

tcf(c_121743,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_112089]) ).

tcf(c_121744,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_111767]) ).

tcf(c_121745,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_111405]) ).

tcf(c_121746,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_111079]) ).

tcf(c_121747,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_110591]) ).

tcf(c_121748,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_109784]) ).

tcf(c_121749,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_109567]) ).

tcf(c_121750,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_108992]) ).

tcf(c_121751,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_107183]) ).

tcf(c_121755,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_106960]) ).

tcf(c_121756,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_105967]) ).

tcf(c_121758,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_95608]) ).

tcf(c_121761,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_120219,c_98014]) ).

tcf(c_121762,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_95414]) ).

tcf(c_121763,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_95286]) ).

tcf(c_121764,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_95041]) ).

tcf(c_121765,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_94695]) ).

tcf(c_121766,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_94594]) ).

tcf(c_121767,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_93822]) ).

tcf(c_121768,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_93551]) ).

tcf(c_121769,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120219,c_79918]) ).

tcf(c_121772,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120219,c_83537]) ).

tcf(c_121773,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120219,c_83534]) ).

tcf(c_121779,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120219,c_96186]) ).

tcf(c_121786,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_121761,c_79573]) ).

tcf(c_121924,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_120957]) ).

tcf(c_121925,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_120957]) ).

tcf(c_121926,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_120957]) ).

tcf(c_121927,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_120957]) ).

tcf(c_121929,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_120957]) ).

tcf(c_121930,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_120957]) ).

tcf(c_121932,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_120957]) ).

tcf(c_121933,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_120957]) ).

tcf(c_121934,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_120957]) ).

tcf(c_121935,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_120957]) ).

tcf(c_121936,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_120957]) ).

tcf(c_121937,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_120957]) ).

tcf(c_121938,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_120957]) ).

tcf(c_121939,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_120957]) ).

tcf(c_121940,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_120957]) ).

tcf(c_121941,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_120957]) ).

tcf(c_121942,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_120957]) ).

tcf(c_121943,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_120957]) ).

tcf(c_121944,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_120957]) ).

tcf(c_121945,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_120957]) ).

tcf(c_121946,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_120957]) ).

tcf(c_121947,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_120957]) ).

tcf(c_121948,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_120957]) ).

tcf(c_121949,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_120957]) ).

tcf(c_121950,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_120957]) ).

tcf(c_121951,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_120957]) ).

tcf(c_121952,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_120957]) ).

tcf(c_121953,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_120957]) ).

tcf(c_121954,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_120957]) ).

tcf(c_121955,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_120957]) ).

tcf(c_121956,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_120957]) ).

tcf(c_121957,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_120957]) ).

tcf(c_121958,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_120957]) ).

tcf(c_121959,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_120957]) ).

tcf(c_121960,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_120957]) ).

tcf(c_121961,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_120957]) ).

tcf(c_121962,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_120957]) ).

tcf(c_121963,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_120957]) ).

tcf(c_121964,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_120957]) ).

tcf(c_121965,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_120957]) ).

tcf(c_121966,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_120957]) ).

tcf(c_121967,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_120957]) ).

tcf(c_121968,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_120957]) ).

tcf(c_121969,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_120957]) ).

tcf(c_121970,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_120957]) ).

tcf(c_121971,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_120957]) ).

tcf(c_121972,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_120957]) ).

tcf(c_121973,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_120957]) ).

tcf(c_121974,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_120957]) ).

tcf(c_121975,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_120957]) ).

tcf(c_121976,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_120957]) ).

tcf(c_121977,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_120957]) ).

tcf(c_121978,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_120957]) ).

tcf(c_121979,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_120957]) ).

tcf(c_121980,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_120957]) ).

tcf(c_121981,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_120957]) ).

tcf(c_121982,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_120957]) ).

tcf(c_121983,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_120957]) ).

tcf(c_121984,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_120957]) ).

tcf(c_121985,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_120957]) ).

tcf(c_121986,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_120957]) ).

tcf(c_121987,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_120957]) ).

tcf(c_121988,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_120957]) ).

tcf(c_121989,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_120957]) ).

tcf(c_121990,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_120957]) ).

tcf(c_121991,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_120957]) ).

tcf(c_121992,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_120957]) ).

tcf(c_121993,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_120957]) ).

tcf(c_121994,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_120957]) ).

tcf(c_121995,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_120957]) ).

tcf(c_121996,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_120957]) ).

tcf(c_121997,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_120957]) ).

tcf(c_121998,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_120957]) ).

tcf(c_121999,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_120957]) ).

tcf(c_122000,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_120957]) ).

tcf(c_122001,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_120957]) ).

tcf(c_122002,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_120957]) ).

tcf(c_122003,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_120957]) ).

tcf(c_122004,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_120957]) ).

tcf(c_122005,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_120957]) ).

tcf(c_122006,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_120957]) ).

tcf(c_122007,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_120957]) ).

tcf(c_122008,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_120957]) ).

tcf(c_122009,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_120957]) ).

tcf(c_122010,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_120957]) ).

tcf(c_122011,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_120957]) ).

tcf(c_122012,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_120957]) ).

tcf(c_122013,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_120957]) ).

tcf(c_122016,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_92656]) ).

tcf(c_122017,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_120957,c_255]) ).

tcf(c_122019,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120957,c_256]) ).

tcf(c_122022,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_120957,c_83532]) ).

tcf(c_122023,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_120957,c_83524]) ).

tcf(c_122024,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_120957]) ).

tcf(c_122025,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_120350]) ).

tcf(c_122026,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_119871]) ).

tcf(c_122027,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_119253]) ).

tcf(c_122028,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_118422]) ).

tcf(c_122029,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_117980]) ).

tcf(c_122030,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_117134]) ).

tcf(c_122031,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_115780]) ).

tcf(c_122032,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_115349]) ).

tcf(c_122033,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_114908]) ).

tcf(c_122034,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_114369]) ).

tcf(c_122035,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_113744]) ).

tcf(c_122036,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_113419]) ).

tcf(c_122037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_112967]) ).

tcf(c_122038,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_112089]) ).

tcf(c_122039,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_111767]) ).

tcf(c_122040,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_111405]) ).

tcf(c_122041,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_111079]) ).

tcf(c_122042,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_110591]) ).

tcf(c_122043,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_109784]) ).

tcf(c_122044,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_109567]) ).

tcf(c_122045,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_108992]) ).

tcf(c_122046,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_107183]) ).

tcf(c_122050,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_106960]) ).

tcf(c_122051,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_105967]) ).

tcf(c_122053,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_95608]) ).

tcf(c_122056,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_120957,c_98014]) ).

tcf(c_122057,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_95414]) ).

tcf(c_122058,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_95286]) ).

tcf(c_122059,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_95041]) ).

tcf(c_122060,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_94695]) ).

tcf(c_122061,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_94594]) ).

tcf(c_122062,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_93822]) ).

tcf(c_122063,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_93551]) ).

tcf(c_122064,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120957,c_79918]) ).

tcf(c_122067,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120957,c_83537]) ).

tcf(c_122068,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120957,c_83534]) ).

tcf(c_122074,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120957,c_96186]) ).

tcf(c_122075,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_121929,c_59636]) ).

tcf(c_122076,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_121924,c_79190]) ).

tcf(c_122077,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122064,c_76415]) ).

tcf(c_122078,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_121932,c_76855,c_93903]) ).

tcf(c_122082,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_122056,c_79573]) ).

tcf(c_122275,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_92656]) ).

tcf(c_122276,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_120823,c_255]) ).

tcf(c_122278,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120823,c_256]) ).

tcf(c_122281,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_120823,c_83532]) ).

tcf(c_122282,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_120823,c_83524]) ).

tcf(c_122283,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_120957]) ).

tcf(c_122284,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_120350]) ).

tcf(c_122285,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_119871]) ).

tcf(c_122286,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_119253]) ).

tcf(c_122287,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_118422]) ).

tcf(c_122288,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_117980]) ).

tcf(c_122289,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_117134]) ).

tcf(c_122290,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_115780]) ).

tcf(c_122291,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_115349]) ).

tcf(c_122292,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_114908]) ).

tcf(c_122293,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_114369]) ).

tcf(c_122294,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_113744]) ).

tcf(c_122295,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_113419]) ).

tcf(c_122296,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_112967]) ).

tcf(c_122297,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_112089]) ).

tcf(c_122298,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_111767]) ).

tcf(c_122299,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_111405]) ).

tcf(c_122300,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_111079]) ).

tcf(c_122301,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_110591]) ).

tcf(c_122302,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_109784]) ).

tcf(c_122303,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_109567]) ).

tcf(c_122304,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_108992]) ).

tcf(c_122305,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_107183]) ).

tcf(c_122309,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_106960]) ).

tcf(c_122310,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_105967]) ).

tcf(c_122312,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_95608]) ).

tcf(c_122315,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_120823,c_98014]) ).

tcf(c_122316,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_95414]) ).

tcf(c_122317,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_95286]) ).

tcf(c_122318,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_95041]) ).

tcf(c_122319,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_94695]) ).

tcf(c_122320,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_94594]) ).

tcf(c_122321,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_93822]) ).

tcf(c_122322,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_93551]) ).

tcf(c_122323,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120823,c_79918]) ).

tcf(c_122326,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120823,c_83537]) ).

tcf(c_122327,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120823,c_83534]) ).

tcf(c_122333,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_120823,c_96186]) ).

tcf(c_122340,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_122315,c_79573]) ).

tcf(c_122383,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_122077]) ).

tcf(c_122384,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_122077]) ).

tcf(c_122385,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_122077]) ).

tcf(c_122386,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_122077]) ).

tcf(c_122388,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_122077]) ).

tcf(c_122389,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_122077]) ).

tcf(c_122391,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_122077]) ).

tcf(c_122392,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_122077]) ).

tcf(c_122393,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_122077]) ).

tcf(c_122394,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_122077]) ).

tcf(c_122395,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_122077]) ).

tcf(c_122396,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_122077]) ).

tcf(c_122397,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_122077]) ).

tcf(c_122398,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_122077]) ).

tcf(c_122399,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_122077]) ).

tcf(c_122400,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_122077]) ).

tcf(c_122401,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_122077]) ).

tcf(c_122402,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_122077]) ).

tcf(c_122403,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_122077]) ).

tcf(c_122404,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_122077]) ).

tcf(c_122405,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_122077]) ).

tcf(c_122406,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_122077]) ).

tcf(c_122407,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_122077]) ).

tcf(c_122408,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_122077]) ).

tcf(c_122409,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_122077]) ).

tcf(c_122410,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_122077]) ).

tcf(c_122411,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_122077]) ).

tcf(c_122412,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_122077]) ).

tcf(c_122413,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_122077]) ).

tcf(c_122414,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_122077]) ).

tcf(c_122415,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_122077]) ).

tcf(c_122416,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_122077]) ).

tcf(c_122417,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_122077]) ).

tcf(c_122418,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_122077]) ).

tcf(c_122419,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_122077]) ).

tcf(c_122420,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_122077]) ).

tcf(c_122421,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_122077]) ).

tcf(c_122422,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_122077]) ).

tcf(c_122423,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_122077]) ).

tcf(c_122424,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_122077]) ).

tcf(c_122425,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_122077]) ).

tcf(c_122426,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_122077]) ).

tcf(c_122427,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_122077]) ).

tcf(c_122428,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_122077]) ).

tcf(c_122429,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_122077]) ).

tcf(c_122430,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_122077]) ).

tcf(c_122431,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_122077]) ).

tcf(c_122432,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_122077]) ).

tcf(c_122433,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_122077]) ).

tcf(c_122434,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_122077]) ).

tcf(c_122435,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_122077]) ).

tcf(c_122436,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_122077]) ).

tcf(c_122437,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_122077]) ).

tcf(c_122438,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_122077]) ).

tcf(c_122439,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_122077]) ).

tcf(c_122440,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_122077]) ).

tcf(c_122441,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_122077]) ).

tcf(c_122442,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_122077]) ).

tcf(c_122443,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_122077]) ).

tcf(c_122444,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_122077]) ).

tcf(c_122445,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_122077]) ).

tcf(c_122446,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_122077]) ).

tcf(c_122447,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_122077]) ).

tcf(c_122448,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_122077]) ).

tcf(c_122449,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_122077]) ).

tcf(c_122450,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_122077]) ).

tcf(c_122451,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_122077]) ).

tcf(c_122452,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_122077]) ).

tcf(c_122453,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_122077]) ).

tcf(c_122454,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_122077]) ).

tcf(c_122455,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_122077]) ).

tcf(c_122456,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_122077]) ).

tcf(c_122457,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_122077]) ).

tcf(c_122458,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_122077]) ).

tcf(c_122459,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_122077]) ).

tcf(c_122460,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_122077]) ).

tcf(c_122461,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_122077]) ).

tcf(c_122462,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_122077]) ).

tcf(c_122463,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_122077]) ).

tcf(c_122464,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_122077]) ).

tcf(c_122465,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_122077]) ).

tcf(c_122466,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_122077]) ).

tcf(c_122467,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_122077]) ).

tcf(c_122468,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_122077]) ).

tcf(c_122469,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_122077]) ).

tcf(c_122470,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_122077]) ).

tcf(c_122471,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_122077]) ).

tcf(c_122472,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_122077]) ).

tcf(c_122473,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_122077]) ).

tcf(c_122474,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_122077]) ).

tcf(c_122477,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_92656]) ).

tcf(c_122478,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_122077,c_255]) ).

tcf(c_122480,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122077,c_256]) ).

tcf(c_122483,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_122077,c_83532]) ).

tcf(c_122484,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_122077,c_83524]) ).

tcf(c_122485,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_122077]) ).

tcf(c_122486,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_120957]) ).

tcf(c_122487,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_120350]) ).

tcf(c_122488,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_119871]) ).

tcf(c_122489,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_119253]) ).

tcf(c_122490,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_118422]) ).

tcf(c_122491,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_117980]) ).

tcf(c_122492,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_117134]) ).

tcf(c_122493,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_115780]) ).

tcf(c_122494,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_115349]) ).

tcf(c_122495,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_114908]) ).

tcf(c_122496,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_114369]) ).

tcf(c_122497,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_113744]) ).

tcf(c_122498,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_113419]) ).

tcf(c_122499,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_112967]) ).

tcf(c_122500,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_112089]) ).

tcf(c_122501,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_111767]) ).

tcf(c_122502,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_111405]) ).

tcf(c_122503,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_111079]) ).

tcf(c_122504,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_110591]) ).

tcf(c_122505,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_109784]) ).

tcf(c_122506,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_109567]) ).

tcf(c_122507,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_108992]) ).

tcf(c_122508,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_107183]) ).

tcf(c_122512,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_106960]) ).

tcf(c_122513,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_105967]) ).

tcf(c_122515,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_95608]) ).

tcf(c_122518,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_122077,c_98014]) ).

tcf(c_122519,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_95414]) ).

tcf(c_122520,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_95286]) ).

tcf(c_122521,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_95041]) ).

tcf(c_122522,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_94695]) ).

tcf(c_122523,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_94594]) ).

tcf(c_122524,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_93822]) ).

tcf(c_122525,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_93551]) ).

tcf(c_122526,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122077,c_79918]) ).

tcf(c_122529,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122077,c_83537]) ).

tcf(c_122530,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122077,c_83534]) ).

tcf(c_122536,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122077,c_96186]) ).

tcf(c_122537,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122388,c_59636]) ).

tcf(c_122538,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122383,c_79190]) ).

tcf(c_122539,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122526,c_76415]) ).

tcf(c_122540,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122391,c_76855,c_93903]) ).

tcf(c_122544,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_122518,c_79573]) ).

tcf(c_122833,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_92656]) ).

tcf(c_122834,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_121940,c_255]) ).

tcf(c_122836,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_121940,c_256]) ).

tcf(c_122839,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_121940,c_83532]) ).

tcf(c_122840,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_121940,c_83524]) ).

tcf(c_122841,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_122077]) ).

tcf(c_122842,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_120957]) ).

tcf(c_122843,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_120350]) ).

tcf(c_122844,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_119871]) ).

tcf(c_122845,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_119253]) ).

tcf(c_122846,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_118422]) ).

tcf(c_122847,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_117980]) ).

tcf(c_122848,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_117134]) ).

tcf(c_122849,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_115780]) ).

tcf(c_122850,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_115349]) ).

tcf(c_122851,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_114908]) ).

tcf(c_122852,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_114369]) ).

tcf(c_122853,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_113744]) ).

tcf(c_122854,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_113419]) ).

tcf(c_122855,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_112967]) ).

tcf(c_122856,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_112089]) ).

tcf(c_122857,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_111767]) ).

tcf(c_122858,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_111405]) ).

tcf(c_122859,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_111079]) ).

tcf(c_122860,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_110591]) ).

tcf(c_122861,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_109784]) ).

tcf(c_122862,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_109567]) ).

tcf(c_122863,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_108992]) ).

tcf(c_122864,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_107183]) ).

tcf(c_122868,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_106960]) ).

tcf(c_122869,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_105967]) ).

tcf(c_122871,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_95608]) ).

tcf(c_122874,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_121940,c_98014]) ).

tcf(c_122875,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_95414]) ).

tcf(c_122876,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_95286]) ).

tcf(c_122877,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_95041]) ).

tcf(c_122878,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_94695]) ).

tcf(c_122879,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_94594]) ).

tcf(c_122880,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_93822]) ).

tcf(c_122881,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_93551]) ).

tcf(c_122882,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_121940,c_79918]) ).

tcf(c_122885,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_121940,c_83537]) ).

tcf(c_122886,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_121940,c_83534]) ).

tcf(c_122892,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_121940,c_96186]) ).

tcf(c_122899,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_122874,c_79573]) ).

tcf(c_122976,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79918,c_122539]) ).

tcf(c_122977,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),X1))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_255,c_122539]) ).

tcf(c_122978,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),one_one_int))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_59636,c_122539]) ).

tcf(c_122979,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_257,c_122539]) ).

tcf(c_122981,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_76874,c_122539]) ).

tcf(c_122982,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_256,c_122539]) ).

tcf(c_122984,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93890,c_122539]) ).

tcf(c_122985,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(plus_plus_int(X0),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(plus_plus_int(X0),X0))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78930,c_122539]) ).

tcf(c_122986,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_15))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_78938,c_122539]) ).

tcf(c_122987,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79190,c_122539]) ).

tcf(c_122988,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(iPr_def_14),X0))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(iPr_def_14),X0))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79161,c_122539]) ).

tcf(c_122989,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(times_times_int(X0),iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(times_times_int(X0),iPr_def_14))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79901,c_122539]) ).

tcf(c_122990,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_13,iPr_def_14))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,hAPP_int_int(iPr_def_12,hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_79904,c_122539]) ).

tcf(c_122991,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83594,c_122539]) ).

tcf(c_122992,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_83616,c_122539]) ).

tcf(c_122993,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_85658,c_122539]) ).

tcf(c_122994,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88494,c_122539]) ).

tcf(c_122995,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88513,c_122539]) ).

tcf(c_122996,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_88550,c_122539]) ).

tcf(c_122997,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92656,c_122539]) ).

tcf(c_122998,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92625,c_122539]) ).

tcf(c_122999,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_92936,c_122539]) ).

tcf(c_123000,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93551,c_122539]) ).

tcf(c_123001,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_93822,c_122539]) ).

tcf(c_123002,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94573,c_122539]) ).

tcf(c_123003,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94594,c_122539]) ).

tcf(c_123004,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94672,c_122539]) ).

tcf(c_123005,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_94695,c_122539]) ).

tcf(c_123006,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95015,c_122539]) ).

tcf(c_123007,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95041,c_122539]) ).

tcf(c_123008,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95257,c_122539]) ).

tcf(c_123009,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95286,c_122539]) ).

tcf(c_123010,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95382,c_122539]) ).

tcf(c_123011,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95414,c_122539]) ).

tcf(c_123012,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95573,c_122539]) ).

tcf(c_123013,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_95608,c_122539]) ).

tcf(c_123014,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_98911,c_122539]) ).

tcf(c_123015,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_99037,c_122539]) ).

tcf(c_123016,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105916,c_122539]) ).

tcf(c_123017,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_105967,c_122539]) ).

tcf(c_123018,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106906,c_122539]) ).

tcf(c_123019,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_106960,c_122539]) ).

tcf(c_123020,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107126,c_122539]) ).

tcf(c_123021,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107183,c_122539]) ).

tcf(c_123022,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_107289,c_122539]) ).

tcf(c_123023,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108926,c_122539]) ).

tcf(c_123024,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_108992,c_122539]) ).

tcf(c_123025,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109498,c_122539]) ).

tcf(c_123026,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109567,c_122539]) ).

tcf(c_123027,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109712,c_122539]) ).

tcf(c_123028,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_109784,c_122539]) ).

tcf(c_123029,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11))),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110344,c_122539]) ).

tcf(c_123030,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110512,c_122539]) ).

tcf(c_123031,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110591,c_122539]) ).

tcf(c_123032,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_110997,c_122539]) ).

tcf(c_123033,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111079,c_122539]) ).

tcf(c_123034,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111320,c_122539]) ).

tcf(c_123035,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111405,c_122539]) ).

tcf(c_123036,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111679,c_122539]) ).

tcf(c_123037,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111767,c_122539]) ).

tcf(c_123038,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_111998,c_122539]) ).

tcf(c_123039,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112089,c_122539]) ).

tcf(c_123040,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112872,c_122539]) ).

tcf(c_123041,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_112967,c_122539]) ).

tcf(c_123042,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113321,c_122539]) ).

tcf(c_123043,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113419,c_122539]) ).

tcf(c_123044,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113643,c_122539]) ).

tcf(c_123045,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_113744,c_122539]) ).

tcf(c_123046,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114265,c_122539]) ).

tcf(c_123047,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114369,c_122539]) ).

tcf(c_123048,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114801,c_122539]) ).

tcf(c_123049,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_114908,c_122539]) ).

tcf(c_123050,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115239,c_122539]) ).

tcf(c_123051,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115349,c_122539]) ).

tcf(c_123052,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115667,c_122539]) ).

tcf(c_123053,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_115780,c_122539]) ).

tcf(c_123054,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117018,c_122539]) ).

tcf(c_123055,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117134,c_122539]) ).

tcf(c_123056,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117861,c_122539]) ).

tcf(c_123057,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_117980,c_122539]) ).

tcf(c_123058,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118300,c_122539]) ).

tcf(c_123059,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_118422,c_122539]) ).

tcf(c_123060,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119128,c_122539]) ).

tcf(c_123061,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119253,c_122539]) ).

tcf(c_123062,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119743,c_122539]) ).

tcf(c_123063,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_119871,c_122539]) ).

tcf(c_123064,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120219,c_122539]) ).

tcf(c_123065,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120350,c_122539]) ).

tcf(c_123066,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120823,c_122539]) ).

tcf(c_123067,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_120957,c_122539]) ).

tcf(c_123068,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_121940,c_122539]) ).

tcf(c_123069,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122077,c_122539]) ).

tcf(c_123072,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_92656]) ).

tcf(c_123073,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X1),
    inference(superposition,[status(thm)],[c_122539,c_255]) ).

tcf(c_123075,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122539,c_256]) ).

tcf(c_123078,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_122539,c_83532]) ).

tcf(c_123079,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),X1)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X1)),
    inference(superposition,[status(thm)],[c_122539,c_83524]) ).

tcf(c_123080,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_122539]) ).

tcf(c_123081,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_122077]) ).

tcf(c_123082,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_120957]) ).

tcf(c_123083,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_120350]) ).

tcf(c_123084,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_119871]) ).

tcf(c_123085,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_119253]) ).

tcf(c_123086,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_118422]) ).

tcf(c_123087,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_117980]) ).

tcf(c_123088,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_117134]) ).

tcf(c_123089,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_115780]) ).

tcf(c_123090,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_115349]) ).

tcf(c_123091,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_114908]) ).

tcf(c_123092,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_114369]) ).

tcf(c_123093,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_113744]) ).

tcf(c_123094,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_113419]) ).

tcf(c_123095,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_112967]) ).

tcf(c_123096,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_112089]) ).

tcf(c_123097,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_111767]) ).

tcf(c_123098,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_111405]) ).

tcf(c_123099,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_111079]) ).

tcf(c_123100,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_110591]) ).

tcf(c_123101,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_109784]) ).

tcf(c_123102,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_109567]) ).

tcf(c_123103,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_108992]) ).

tcf(c_123104,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_107183]) ).

tcf(c_123108,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_106960]) ).

tcf(c_123109,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_105967]) ).

tcf(c_123111,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_95608]) ).

tcf(c_123114,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_122539,c_98014]) ).

tcf(c_123115,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_95414]) ).

tcf(c_123116,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_95286]) ).

tcf(c_123117,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_95041]) ).

tcf(c_123118,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_94695]) ).

tcf(c_123119,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_94594]) ).

tcf(c_123120,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_93822]) ).

tcf(c_123121,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122539,c_93551]) ).

tcf(c_123122,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122539,c_79918]) ).

tcf(c_123125,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122539,c_83537]) ).

tcf(c_123126,plain,
    ! [X0: $i,X1: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1)))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122539,c_83534]) ).

tcf(c_123132,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122539,c_96186]) ).

tcf(c_123133,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(iPr_def_12,hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,m))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122981,c_59636]) ).

tcf(c_123134,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,iPr_def_14))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122976,c_79190]) ).

tcf(c_123135,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_123122,c_76415]) ).

tcf(c_123136,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(light_normalisation,[status(thm)],[c_122984,c_76855,c_93903]) ).

tcf(c_123140,plain,
    ! [X0: $i,X1: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X1))))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_123114,c_79573]) ).

tcf(c_123479,plain,
    hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_92656]) ).

tcf(c_123480,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),X0),
    inference(superposition,[status(thm)],[c_122399,c_255]) ).

tcf(c_123482,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(plus_plus_int(X0),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122399,c_256]) ).

tcf(c_123485,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_122399,c_83532]) ).

tcf(c_123486,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),X0)) = hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)),
    inference(superposition,[status(thm)],[c_122399,c_83524]) ).

tcf(c_123487,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_122539]) ).

tcf(c_123488,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_122077]) ).

tcf(c_123489,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_120957]) ).

tcf(c_123490,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_120350]) ).

tcf(c_123491,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_119871]) ).

tcf(c_123492,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_119253]) ).

tcf(c_123493,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_118422]) ).

tcf(c_123494,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_117980]) ).

tcf(c_123495,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_117134]) ).

tcf(c_123496,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_115780]) ).

tcf(c_123497,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_115349]) ).

tcf(c_123498,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_114908]) ).

tcf(c_123499,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_114369]) ).

tcf(c_123500,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_113744]) ).

tcf(c_123501,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_113419]) ).

tcf(c_123502,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_112967]) ).

tcf(c_123503,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_112089]) ).

tcf(c_123504,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_111767]) ).

tcf(c_123505,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_111405]) ).

tcf(c_123506,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_111079]) ).

tcf(c_123507,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_110591]) ).

tcf(c_123508,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_109784]) ).

tcf(c_123509,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_109567]) ).

tcf(c_123510,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_108992]) ).

tcf(c_123511,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_107183]) ).

tcf(c_123515,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_106960]) ).

tcf(c_123516,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_105967]) ).

tcf(c_123518,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_95608]) ).

tcf(c_123521,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))),
    inference(superposition,[status(thm)],[c_122399,c_98014]) ).

tcf(c_123522,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_95414]) ).

tcf(c_123523,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_95286]) ).

tcf(c_123524,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_95041]) ).

tcf(c_123525,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_94695]) ).

tcf(c_123526,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_94594]) ).

tcf(c_123527,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_93822]) ).

tcf(c_123528,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19),
    inference(superposition,[status(thm)],[c_122399,c_93551]) ).

tcf(c_123529,plain,
    hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = number_number_of_int(sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122399,c_79918]) ).

tcf(c_123532,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122399,c_83537]) ).

tcf(c_123533,plain,
    ! [X0: $i] : number_number_of_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))))) = hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122399,c_83534]) ).

tcf(c_123539,plain,
    hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),sK30(iPr_def_19)),
    inference(superposition,[status(thm)],[c_122399,c_96186]) ).

tcf(c_123546,plain,
    ! [X0: $i] : hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))))),m)))) = hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),
    inference(light_normalisation,[status(thm)],[c_123521,c_79573]) ).

tcf(c_123611,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(number_number_of_nat(min)),number_number_of_nat(X0)) = number_number_of_nat(X0),
    inference(superposition,[status(thm)],[c_768,c_175]) ).

tcf(c_123612,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(X1) )
      | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_175]) ).

tcf(c_123614,plain,
    ! [X0: $i] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),number_number_of_nat(X0)) = number_number_of_nat(X0),
    inference(light_normalisation,[status(thm)],[c_123611,c_78282]) ).

tcf(c_123625,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_nat_int(power_power_int(X0),iPr_def_11)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(superposition,[status(thm)],[c_82861,c_198]) ).

tcf(c_123628,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X2))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_252,c_198]) ).

tcf(c_123629,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X2),X1))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X2))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X0),X1))) ),
    inference(superposition,[status(thm)],[c_217,c_198]) ).

tcf(c_123632,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(hAPP_int_int(times_times_int(X0),X1))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(X0))) ),
    inference(superposition,[status(thm)],[c_382,c_198]) ).

tcf(c_123634,plain,
    ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,one_one_int))
    | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,min)) ),
    inference(superposition,[status(thm)],[c_79464,c_198]) ).

tcf(c_123644,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(plus_plus_int(X0),X0)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,iPr_def_14))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(superposition,[status(thm)],[c_79150,c_198]) ).

tcf(c_123645,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83532,c_198]) ).

tcf(c_123646,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(m),X0)))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(X1)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))) ),
    inference(superposition,[status(thm)],[c_83537,c_198]) ).

tcf(c_123650,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(plus_plus_int(m),number_number_of_int(number_number_of_int(X0))))) ),
    inference(superposition,[status(thm)],[c_96186,c_198]) ).

tcf(c_123651,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))) ),
    inference(superposition,[status(thm)],[c_98014,c_198]) ).

tcf(c_123652,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))) ),
    inference(superposition,[status(thm)],[c_98014,c_198]) ).

tcf(c_123653,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1)))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))))) ),
    inference(superposition,[status(thm)],[c_106496,c_198]) ).

tcf(c_123654,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m))))))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,sK30(iPr_def_19)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,number_number_of_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))))) ),
    inference(superposition,[status(thm)],[c_106728,c_198]) ).

tcf(c_123657,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(iPr_def_13,X0)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,m))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(superposition,[status(thm)],[c_59637,c_198]) ).

tcf(c_123658,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK23(hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_198,c_1488]) ).

tcf(c_123659,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK22(hAPP_int_int(times_times_int(X0),X1)))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0))
      | ~ is_int(hAPP_int_int(times_times_int(X0),X1)) ),
    inference(superposition,[status(thm)],[c_198,c_1487]) ).

tcf(c_123660,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(member_int(hAPP_int_int(times_times_int(X1),X0),twoSqu1154269391sum2sq))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X1))
      | ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X0)) ),
    inference(superposition,[status(thm)],[c_198,c_226]) ).

tcf(c_123790,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(pls)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != pls ) ),
    inference(superposition,[status(thm)],[c_574,c_245]) ).

tcf(c_123791,plain,
    ! [X0: $i] :
      ( ( X0 = min )
      | ~ is_int(min)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != min ) ),
    inference(superposition,[status(thm)],[c_76397,c_245]) ).

tcf(c_123792,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(one_one_int)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != one_one_int ) ),
    inference(superposition,[status(thm)],[c_76393,c_245]) ).

tcf(c_123793,plain,
    ! [X0: $i] :
      ( ( undefined_int(int) = X0 )
      | ~ is_int(X0)
      | ~ is_int(undefined_int(int))
      | ( number_number_of_int(X0) != undefined_int(int) ) ),
    inference(superposition,[status(thm)],[c_76395,c_245]) ).

tcf(c_123794,plain,
    ! [X0: $i,X1: $i] :
      ( ( twoSqu1241645765sum2sq(X1) = X0 )
      | ~ is_int(X0)
      | ~ is_int(twoSqu1241645765sum2sq(X1))
      | ( number_number_of_int(X0) != twoSqu1241645765sum2sq(X1) ) ),
    inference(superposition,[status(thm)],[c_76399,c_245]) ).

tcf(c_123795,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(X0,X1) = X2 )
      | ~ is_int(X2)
      | ~ is_int(hAPP_nat_int(X0,X1))
      | ( hAPP_nat_int(X0,X1) != number_number_of_int(X2) ) ),
    inference(superposition,[status(thm)],[c_76401,c_245]) ).

tcf(c_123796,plain,
    ! [X0: $i] :
      ( ( X0 = m )
      | ~ is_int(m)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != m ) ),
    inference(superposition,[status(thm)],[c_76402,c_245]) ).

tcf(c_123797,plain,
    ! [X0: $i] :
      ( ( X0 = s1 )
      | ~ is_int(s1)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != s1 ) ),
    inference(superposition,[status(thm)],[c_76403,c_245]) ).

tcf(c_123798,plain,
    ! [X0: $i] :
      ( ( X0 = s )
      | ~ is_int(s)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != s ) ),
    inference(superposition,[status(thm)],[c_76404,c_245]) ).

tcf(c_123799,plain,
    ! [X0: $i] :
      ( ( X0 = t )
      | ~ is_int(t)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != t ) ),
    inference(superposition,[status(thm)],[c_76405,c_245]) ).

tcf(c_123800,plain,
    ! [X0: $i] :
      ( ( X0 = sK9 )
      | ~ is_int(sK9)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK9 ) ),
    inference(superposition,[status(thm)],[c_76406,c_245]) ).

tcf(c_123801,plain,
    ! [X0: $i] :
      ( ( X0 = sK10 )
      | ~ is_int(sK10)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK10 ) ),
    inference(superposition,[status(thm)],[c_76407,c_245]) ).

tcf(c_123802,plain,
    ! [X0: $i] :
      ( ( X0 = sK11 )
      | ~ is_int(sK11)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK11 ) ),
    inference(superposition,[status(thm)],[c_76408,c_245]) ).

tcf(c_123803,plain,
    ! [X0: $i] :
      ( ( X0 = sK13 )
      | ~ is_int(sK13)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK13 ) ),
    inference(superposition,[status(thm)],[c_76409,c_245]) ).

tcf(c_123804,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_14 )
      | ~ is_int(iPr_def_14)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_14 ) ),
    inference(superposition,[status(thm)],[c_76410,c_245]) ).

tcf(c_123805,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_15 )
      | ~ is_int(iPr_def_15)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_15 ) ),
    inference(superposition,[status(thm)],[c_76411,c_245]) ).

tcf(c_123806,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_16 )
      | ~ is_int(iPr_def_16)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_16 ) ),
    inference(superposition,[status(thm)],[c_76412,c_245]) ).

tcf(c_123807,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_17 )
      | ~ is_int(iPr_def_17)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_17 ) ),
    inference(superposition,[status(thm)],[c_76413,c_245]) ).

tcf(c_123808,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_18 )
      | ~ is_int(iPr_def_18)
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_76414,c_245]) ).

tcf(c_123809,plain,
    ! [X0: $i] :
      ( ( sK30(iPr_def_19) = X0 )
      | ~ is_int(X0)
      | ~ is_int(sK30(iPr_def_19))
      | ( number_number_of_int(X0) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76415,c_245]) ).

tcf(c_123810,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(iPr_def_13,X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(iPr_def_13,X0))
      | ( hAPP_int_int(iPr_def_13,X0) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_77366,c_245]) ).

tcf(c_123811,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(iPr_def_12,X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(iPr_def_12,X0))
      | ( hAPP_int_int(iPr_def_12,X0) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_78024,c_245]) ).

tcf(c_123812,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK27(X0,t) = X1 )
      | ~ is_int(X1)
      | ~ is_int(sK27(X0,t))
      | ( sK27(X0,t) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_78042,c_245]) ).

tcf(c_123813,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK27(X0,one_one_int) = X1 )
      | ~ is_int(X1)
      | ~ is_int(sK27(X0,one_one_int))
      | ( sK27(X0,one_one_int) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_78056,c_245]) ).

tcf(c_123814,plain,
    ! [X0: $i] :
      ( ( sK26(iPr_def_14) = X0 )
      | ~ is_int(X0)
      | ~ is_int(sK26(iPr_def_14))
      | ( number_number_of_int(X0) != sK26(iPr_def_14) ) ),
    inference(superposition,[status(thm)],[c_78203,c_245]) ).

tcf(c_123815,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_79573,c_245]) ).

tcf(c_123816,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_79414,c_245]) ).

tcf(c_123817,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_79557,c_245]) ).

tcf(c_123818,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_79437,c_245]) ).

tcf(c_123819,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(plus_plus_int(m),X0))
      | ( hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_79918,c_245]) ).

tcf(c_123820,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),m) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),m))
      | ( hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_83504,c_245]) ).

tcf(c_123821,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(m),X0))
      | ( hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_80664,c_245]) ).

tcf(c_123822,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_80677,c_245]) ).

tcf(c_123823,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),m) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),m))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_80692,c_245]) ).

tcf(c_123824,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_80705,c_245]) ).

tcf(c_123825,plain,
    ! [X0: $i] :
      ( ( sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) = X0 )
      | ~ is_int(X0)
      | ~ is_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ( sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X0) ) ),
    inference(superposition,[status(thm)],[c_88502,c_245]) ).

tcf(c_123826,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ~ is_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ( sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_88521,c_245]) ).

tcf(c_123827,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ~ is_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)))
      | ( sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_88558,c_245]) ).

tcf(c_123828,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_96714,c_245]) ).

tcf(c_123829,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_99171,c_245]) ).

tcf(c_123830,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_100498,c_245]) ).

tcf(c_123831,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) != number_number_of_int(X1) ) ),
    inference(superposition,[status(thm)],[c_103848,c_245]) ).

tcf(c_123833,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_18 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_18 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123808,c_76350]) ).

tcf(c_123837,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_17 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_17 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123807,c_76349]) ).

tcf(c_123841,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_16 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_16 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123806,c_76348]) ).

tcf(c_123845,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_15 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_15 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123805,c_76347]) ).

tcf(c_123849,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_14 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != iPr_def_14 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123804,c_76346]) ).

tcf(c_123853,plain,
    ! [X0: $i] :
      ( ( X0 = sK13 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK13 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123803,c_735]) ).

tcf(c_123857,plain,
    ! [X0: $i] :
      ( ( X0 = sK11 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK11 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123802,c_459]) ).

tcf(c_123861,plain,
    ! [X0: $i] :
      ( ( X0 = sK10 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK10 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123801,c_451]) ).

tcf(c_123865,plain,
    ! [X0: $i] :
      ( ( X0 = sK9 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK9 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123800,c_113]) ).

tcf(c_123869,plain,
    ! [X0: $i] :
      ( ( X0 = t )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != t ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123799,c_73]) ).

tcf(c_123873,plain,
    ! [X0: $i] :
      ( ( X0 = s )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != s ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123798,c_72]) ).

tcf(c_123877,plain,
    ! [X0: $i] :
      ( ( X0 = s1 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != s1 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123797,c_71]) ).

tcf(c_123881,plain,
    ! [X0: $i] :
      ( ( X0 = m )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != m ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123796,c_70]) ).

tcf(c_123885,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != one_one_int ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123792,c_49]) ).

tcf(c_123889,plain,
    ! [X0: $i] :
      ( ( X0 = min )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != min ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123791,c_56]) ).

tcf(c_123893,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != pls ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123790,c_57]) ).

tcf(c_123897,plain,
    ! [X0: $i] :
      ( ( sK26(iPr_def_14) = X0 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK26(iPr_def_14) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123814,c_78196]) ).

tcf(c_123901,plain,
    ! [X0: $i] :
      ( ( sK30(iPr_def_19) = X0 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123809,c_76385]) ).

tcf(c_123905,plain,
    ! [X0: $i,X1: $i] :
      ( ( twoSqu1241645765sum2sq(X1) = X0 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != twoSqu1241645765sum2sq(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123794,c_61]) ).

tcf(c_123909,plain,
    ! [X0: $i] :
      ( ( undefined_int(int) = X0 )
      | ~ is_int(X0)
      | ( number_number_of_int(X0) != undefined_int(int) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123793,c_51]) ).

tcf(c_123913,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK27(X0,one_one_int) = X1 )
      | ~ is_int(X1)
      | ( sK27(X0,one_one_int) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123813,c_78001]) ).

tcf(c_123917,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK27(X0,t) = X1 )
      | ~ is_int(X1)
      | ( sK27(X0,t) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123812,c_78000]) ).

tcf(c_123921,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(iPr_def_12,X0) = X1 )
      | ~ is_int(X1)
      | ( hAPP_int_int(iPr_def_12,X0) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123811,c_77937]) ).

tcf(c_123925,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(iPr_def_13,X0) = X1 )
      | ~ is_int(X1)
      | ( hAPP_int_int(iPr_def_13,X0) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123810,c_77054]) ).

tcf(c_123929,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(X0,X1) = X2 )
      | ~ is_int(X2)
      | ( hAPP_nat_int(X0,X1) != number_number_of_int(X2) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123795,c_67]) ).

tcf(c_123989,plain,
    ! [X0: $i] :
      ( ( sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) = X0 )
      | ~ is_int(X0)
      | ( sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123825,c_88316]) ).

tcf(c_123993,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ( sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123827,c_88320]) ).

tcf(c_123997,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)) = X1 )
      | ~ is_int(X1)
      | ( sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19)) != number_number_of_int(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_123826,c_88319]) ).

tcf(c_124074,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),X0)) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_46106]) ).

tcf(c_124075,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(t,hAPP_int_int(iPr_def_13,t),t))),X0) = pls,
    inference(superposition,[status(thm)],[c_121707,c_46104]) ).

tcf(c_124076,plain,
    hAPP_int_int(minus_minus_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),pls) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_880]) ).

tcf(c_124077,plain,
    hAPP_nat_int(power_power_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),one_one_nat) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_608]) ).

tcf(c_124078,plain,
    hAPP_int_int(plus_plus_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),pls) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_524]) ).

tcf(c_124079,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(t,hAPP_int_int(iPr_def_13,t),t)) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_523]) ).

tcf(c_124080,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(t,hAPP_int_int(iPr_def_13,t),t)) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_347]) ).

tcf(c_124081,plain,
    hAPP_int_int(times_times_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)),one_one_int) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_346]) ).

tcf(c_124082,plain,
    number_number_of_int(sK14(t,hAPP_int_int(iPr_def_13,t),t)) = sK14(t,hAPP_int_int(iPr_def_13,t),t),
    inference(superposition,[status(thm)],[c_121707,c_254]) ).

tcf(c_124102,plain,
    hBOOL(member_int(t,zcong(hAPP_int_int(iPr_def_13,t),t))),
    inference(superposition,[status(thm)],[c_121706,c_226]) ).

tcf(c_124103,plain,
    ( is_int(sK14(hAPP_int_int(iPr_def_13,t),t,t))
    | ~ is_int(t) ),
    inference(superposition,[status(thm)],[c_121706,c_852]) ).

tcf(c_124105,plain,
    is_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),
    inference(forward_subsumption_resolution,[status(thm)],[c_124103,c_73]) ).

tcf(c_124106,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),X0)) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_46106]) ).

tcf(c_124107,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(hAPP_int_int(iPr_def_13,t),t,t))),X0) = pls,
    inference(superposition,[status(thm)],[c_124105,c_46104]) ).

tcf(c_124108,plain,
    hAPP_int_int(minus_minus_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),pls) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_880]) ).

tcf(c_124109,plain,
    hAPP_nat_int(power_power_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),one_one_nat) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_608]) ).

tcf(c_124110,plain,
    hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),pls) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_524]) ).

tcf(c_124111,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(hAPP_int_int(iPr_def_13,t),t,t)) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_523]) ).

tcf(c_124112,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(hAPP_int_int(iPr_def_13,t),t,t)) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_347]) ).

tcf(c_124113,plain,
    hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)),one_one_int) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_346]) ).

tcf(c_124114,plain,
    number_number_of_int(sK14(hAPP_int_int(iPr_def_13,t),t,t)) = sK14(hAPP_int_int(iPr_def_13,t),t,t),
    inference(superposition,[status(thm)],[c_124105,c_254]) ).

tcf(c_124132,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_123901]) ).

tcf(c_124133,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_123901]) ).

tcf(c_124134,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_123901]) ).

tcf(c_124135,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_123901]) ).

tcf(c_124136,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),X0))
      | ( hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_123901]) ).

tcf(c_124137,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),m))
      | ( hAPP_int_int(plus_plus_int(m),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_123901]) ).

tcf(c_124138,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),X0))
      | ( hAPP_int_int(minus_minus_int(m),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_123901]) ).

tcf(c_124139,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0))
      | ( hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_123901]) ).

tcf(c_124140,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),m))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_123901]) ).

tcf(c_124141,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19)))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_123901]) ).

tcf(c_124145,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_123901]) ).

tcf(c_124146,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_123901]) ).

tcf(c_124147,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ( hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_123901]) ).

tcf(c_124148,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_123901]) ).

tcf(c_124227,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))) ),
    inference(superposition,[status(thm)],[c_93551,c_124136]) ).

tcf(c_124229,plain,
    ( ( hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))) ),
    inference(superposition,[status(thm)],[c_94573,c_124136]) ).

tcf(c_124320,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124136]) ).

tcf(c_124321,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124136]) ).

tcf(c_124322,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124136]) ).

tcf(c_124323,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124136]) ).

tcf(c_124324,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124136]) ).

tcf(c_124325,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(X0),m)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124136]) ).

tcf(c_124326,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124136]) ).

tcf(c_124327,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124136]) ).

tcf(c_124328,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),m)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124136]) ).

tcf(c_124329,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124136]) ).

tcf(c_124333,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124136]) ).

tcf(c_124334,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124136]) ).

tcf(c_124335,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124136]) ).

tcf(c_124336,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124136]) ).

tcf(c_124343,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(iPr_def_13,iPr_def_14)))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_124325,c_92932]) ).

tcf(c_124347,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,iPr_def_14)),X0))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_124324,c_92621]) ).

tcf(c_124408,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))),m)) ),
    inference(superposition,[status(thm)],[c_93551,c_124137]) ).

tcf(c_124409,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))),m)) ),
    inference(superposition,[status(thm)],[c_93822,c_124137]) ).

tcf(c_124410,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))),m)) ),
    inference(superposition,[status(thm)],[c_94573,c_124137]) ).

tcf(c_124411,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))),m)) ),
    inference(superposition,[status(thm)],[c_94594,c_124137]) ).

tcf(c_124412,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))),m)) ),
    inference(superposition,[status(thm)],[c_94672,c_124137]) ).

tcf(c_124413,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))),m)) ),
    inference(superposition,[status(thm)],[c_94695,c_124137]) ).

tcf(c_124414,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))),m)) ),
    inference(superposition,[status(thm)],[c_95015,c_124137]) ).

tcf(c_124415,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))),m)) ),
    inference(superposition,[status(thm)],[c_95041,c_124137]) ).

tcf(c_124416,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))),m)) ),
    inference(superposition,[status(thm)],[c_95257,c_124137]) ).

tcf(c_124417,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))),m)) ),
    inference(superposition,[status(thm)],[c_95286,c_124137]) ).

tcf(c_124418,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))),m)) ),
    inference(superposition,[status(thm)],[c_95382,c_124137]) ).

tcf(c_124419,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))),m)) ),
    inference(superposition,[status(thm)],[c_95414,c_124137]) ).

tcf(c_124420,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))),m)) ),
    inference(superposition,[status(thm)],[c_95573,c_124137]) ).

tcf(c_124421,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_95608,c_124137]) ).

tcf(c_124422,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_105916,c_124137]) ).

tcf(c_124423,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_105967,c_124137]) ).

tcf(c_124424,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_106906,c_124137]) ).

tcf(c_124425,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_106960,c_124137]) ).

tcf(c_124426,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_107126,c_124137]) ).

tcf(c_124427,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_107183,c_124137]) ).

tcf(c_124428,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_108926,c_124137]) ).

tcf(c_124429,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_108992,c_124137]) ).

tcf(c_124430,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_109498,c_124137]) ).

tcf(c_124431,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_109567,c_124137]) ).

tcf(c_124432,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_109712,c_124137]) ).

tcf(c_124433,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_109784,c_124137]) ).

tcf(c_124434,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_110512,c_124137]) ).

tcf(c_124435,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_110591,c_124137]) ).

tcf(c_124436,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_110997,c_124137]) ).

tcf(c_124437,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111079,c_124137]) ).

tcf(c_124438,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111320,c_124137]) ).

tcf(c_124439,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111405,c_124137]) ).

tcf(c_124440,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111679,c_124137]) ).

tcf(c_124441,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111767,c_124137]) ).

tcf(c_124442,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_111998,c_124137]) ).

tcf(c_124443,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_112089,c_124137]) ).

tcf(c_124444,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_112872,c_124137]) ).

tcf(c_124445,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_112967,c_124137]) ).

tcf(c_124446,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_113321,c_124137]) ).

tcf(c_124447,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_113419,c_124137]) ).

tcf(c_124448,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_113643,c_124137]) ).

tcf(c_124449,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_113744,c_124137]) ).

tcf(c_124450,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_114265,c_124137]) ).

tcf(c_124451,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_114369,c_124137]) ).

tcf(c_124452,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_114801,c_124137]) ).

tcf(c_124453,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_114908,c_124137]) ).

tcf(c_124454,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_115239,c_124137]) ).

tcf(c_124455,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_115349,c_124137]) ).

tcf(c_124456,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_115667,c_124137]) ).

tcf(c_124457,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_115780,c_124137]) ).

tcf(c_124458,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_117018,c_124137]) ).

tcf(c_124459,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_117134,c_124137]) ).

tcf(c_124460,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_117861,c_124137]) ).

tcf(c_124461,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_117980,c_124137]) ).

tcf(c_124462,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_118300,c_124137]) ).

tcf(c_124463,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_118422,c_124137]) ).

tcf(c_124464,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_119128,c_124137]) ).

tcf(c_124465,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_119253,c_124137]) ).

tcf(c_124466,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_119743,c_124137]) ).

tcf(c_124467,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_119871,c_124137]) ).

tcf(c_124468,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_120219,c_124137]) ).

tcf(c_124469,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_120350,c_124137]) ).

tcf(c_124470,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_120823,c_124137]) ).

tcf(c_124471,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_120957,c_124137]) ).

tcf(c_124472,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19)))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_121940,c_124137]) ).

tcf(c_124473,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0))))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_122077,c_124137]) ).

tcf(c_124474,plain,
    ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),m)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),sK30(iPr_def_19))))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_122399,c_124137]) ).

tcf(c_124475,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(number_number_of_int(hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))))))))))))))))))))))))))))))))))))),m)) ),
    inference(superposition,[status(thm)],[c_122539,c_124137]) ).

tcf(c_124476,plain,
    ( ( hAPP_int_int(plus_plus_int(pls),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(pls),m))
    | ( hAPP_int_int(plus_plus_int(m),pls) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_574,c_124137]) ).

tcf(c_124477,plain,
    ( ( hAPP_int_int(plus_plus_int(min),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(min),m))
    | ( hAPP_int_int(plus_plus_int(m),min) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76397,c_124137]) ).

tcf(c_124478,plain,
    ( ( hAPP_int_int(plus_plus_int(one_one_int),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(one_one_int),m))
    | ( hAPP_int_int(plus_plus_int(m),one_one_int) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76393,c_124137]) ).

tcf(c_124479,plain,
    ( ( hAPP_int_int(plus_plus_int(undefined_int(int)),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(undefined_int(int)),m))
    | ( hAPP_int_int(plus_plus_int(m),undefined_int(int)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76395,c_124137]) ).

tcf(c_124480,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(twoSqu1241645765sum2sq(X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),twoSqu1241645765sum2sq(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76399,c_124137]) ).

tcf(c_124481,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(X0,X1)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(X0,X1)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_nat_int(X0,X1)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76401,c_124137]) ).

tcf(c_124483,plain,
    ( ( hAPP_int_int(plus_plus_int(s1),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(s1),m))
    | ( hAPP_int_int(plus_plus_int(m),s1) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76403,c_124137]) ).

tcf(c_124484,plain,
    ( ( hAPP_int_int(plus_plus_int(s),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(s),m))
    | ( hAPP_int_int(plus_plus_int(m),s) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76404,c_124137]) ).

tcf(c_124485,plain,
    ( ( hAPP_int_int(plus_plus_int(t),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(t),m))
    | ( hAPP_int_int(plus_plus_int(m),t) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76405,c_124137]) ).

tcf(c_124486,plain,
    ( ( hAPP_int_int(plus_plus_int(sK9),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK9),m))
    | ( hAPP_int_int(plus_plus_int(m),sK9) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76406,c_124137]) ).

tcf(c_124487,plain,
    ( ( hAPP_int_int(plus_plus_int(sK10),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK10),m))
    | ( hAPP_int_int(plus_plus_int(m),sK10) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76407,c_124137]) ).

tcf(c_124488,plain,
    ( ( hAPP_int_int(plus_plus_int(sK11),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK11),m))
    | ( hAPP_int_int(plus_plus_int(m),sK11) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76408,c_124137]) ).

tcf(c_124489,plain,
    ( ( hAPP_int_int(plus_plus_int(sK13),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK13),m))
    | ( hAPP_int_int(plus_plus_int(m),sK13) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76409,c_124137]) ).

tcf(c_124490,plain,
    ( ( hAPP_int_int(plus_plus_int(iPr_def_14),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(iPr_def_14),m))
    | ( hAPP_int_int(plus_plus_int(m),iPr_def_14) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76410,c_124137]) ).

tcf(c_124491,plain,
    ( ( hAPP_int_int(plus_plus_int(iPr_def_15),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(iPr_def_15),m))
    | ( hAPP_int_int(plus_plus_int(m),iPr_def_15) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76411,c_124137]) ).

tcf(c_124492,plain,
    ( ( hAPP_int_int(plus_plus_int(iPr_def_16),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(iPr_def_16),m))
    | ( hAPP_int_int(plus_plus_int(m),iPr_def_16) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76412,c_124137]) ).

tcf(c_124493,plain,
    ( ( hAPP_int_int(plus_plus_int(iPr_def_17),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(iPr_def_17),m))
    | ( hAPP_int_int(plus_plus_int(m),iPr_def_17) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76413,c_124137]) ).

tcf(c_124494,plain,
    ( ( hAPP_int_int(plus_plus_int(iPr_def_18),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(iPr_def_18),m))
    | ( hAPP_int_int(plus_plus_int(m),iPr_def_18) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76414,c_124137]) ).

tcf(c_124495,plain,
    ( ( hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m))
    | ( hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76415,c_124137]) ).

tcf(c_124496,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_13,X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_77366,c_124137]) ).

tcf(c_124497,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_12,X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(iPr_def_12,X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78024,c_124137]) ).

tcf(c_124498,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK27(X0,t)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(sK27(X0,t)),m))
      | ( hAPP_int_int(plus_plus_int(m),sK27(X0,t)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78042,c_124137]) ).

tcf(c_124499,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK27(X0,one_one_int)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(sK27(X0,one_one_int)),m))
      | ( hAPP_int_int(plus_plus_int(m),sK27(X0,one_one_int)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78056,c_124137]) ).

tcf(c_124500,plain,
    ( ( hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK26(iPr_def_14)),m))
    | ( hAPP_int_int(plus_plus_int(m),sK26(iPr_def_14)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78203,c_124137]) ).

tcf(c_124501,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124137]) ).

tcf(c_124502,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124137]) ).

tcf(c_124503,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124137]) ).

tcf(c_124504,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124137]) ).

tcf(c_124505,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(m),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124137]) ).

tcf(c_124506,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),m)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),m)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124137]) ).

tcf(c_124507,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(m),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124137]) ).

tcf(c_124508,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124137]) ).

tcf(c_124509,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),m)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),m)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124137]) ).

tcf(c_124510,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124137]) ).

tcf(c_124511,plain,
    ( ( hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))
    | ( hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88502,c_124137]) ).

tcf(c_124512,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88521,c_124137]) ).

tcf(c_124513,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(plus_plus_int(m),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88558,c_124137]) ).

tcf(c_124514,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124137]) ).

tcf(c_124515,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124137]) ).

tcf(c_124516,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124137]) ).

tcf(c_124517,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m))
      | ( hAPP_int_int(plus_plus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124137]) ).

tcf(c_124554,plain,
    ( ( hAPP_int_int(iPr_def_12,m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(iPr_def_12,m))
    | ( hAPP_int_int(plus_plus_int(m),one_one_int) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_124478,c_59636]) ).

tcf(c_124555,plain,
    ( ( hAPP_int_int(iPr_def_12,m) = sK30(iPr_def_19) )
    | ( hAPP_int_int(plus_plus_int(m),one_one_int) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_124554,c_77937]) ).

tcf(c_124561,plain,
    ( ( sK30(iPr_def_19) = m )
    | ~ is_int(m)
    | ( hAPP_int_int(plus_plus_int(m),pls) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_124476,c_77148]) ).

tcf(c_124562,plain,
    ( ( sK30(iPr_def_19) = m )
    | ( hAPP_int_int(plus_plus_int(m),pls) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_124561,c_70]) ).

tcf(c_124568,plain,
    ( ( hAPP_int_int(plus_plus_int(sK30(iPr_def_19)),m) = sK30(iPr_def_19) )
    | ( hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_124495,c_93345]) ).

tcf(c_125018,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124138]) ).

tcf(c_125019,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124138]) ).

tcf(c_125020,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124138]) ).

tcf(c_125021,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124138]) ).

tcf(c_125022,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124138]) ).

tcf(c_125023,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(X0),m)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124138]) ).

tcf(c_125024,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124138]) ).

tcf(c_125025,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124138]) ).

tcf(c_125026,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),m)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124138]) ).

tcf(c_125027,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124138]) ).

tcf(c_125031,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124138]) ).

tcf(c_125032,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124138]) ).

tcf(c_125033,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124138]) ).

tcf(c_125034,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(minus_minus_int(m),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124138]) ).

tcf(c_125163,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124140]) ).

tcf(c_125164,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124140]) ).

tcf(c_125165,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124140]) ).

tcf(c_125166,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124140]) ).

tcf(c_125167,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124140]) ).

tcf(c_125168,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),m)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(X0),m)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124140]) ).

tcf(c_125169,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124140]) ).

tcf(c_125170,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124140]) ).

tcf(c_125171,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),m)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),m)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124140]) ).

tcf(c_125172,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124140]) ).

tcf(c_125176,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124140]) ).

tcf(c_125177,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124140]) ).

tcf(c_125178,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124140]) ).

tcf(c_125179,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m))
      | ( hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124140]) ).

tcf(c_125260,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls))
    | ( hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_574,c_124132]) ).

tcf(c_125261,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),min) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),min))
    | ( hAPP_int_int(times_times_int(min),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76397,c_124132]) ).

tcf(c_125262,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int))
    | ( hAPP_int_int(times_times_int(one_one_int),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76393,c_124132]) ).

tcf(c_125263,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)))
    | ( hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76395,c_124132]) ).

tcf(c_125264,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)))
      | ( hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76399,c_124132]) ).

tcf(c_125265,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)))
      | ( hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76401,c_124132]) ).

tcf(c_125266,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))
    | ( hAPP_int_int(times_times_int(m),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76402,c_124132]) ).

tcf(c_125267,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1))
    | ( hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76403,c_124132]) ).

tcf(c_125268,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),s) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),s))
    | ( hAPP_int_int(times_times_int(s),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76404,c_124132]) ).

tcf(c_125269,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),t) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),t))
    | ( hAPP_int_int(times_times_int(t),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76405,c_124132]) ).

tcf(c_125270,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9))
    | ( hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76406,c_124132]) ).

tcf(c_125271,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10))
    | ( hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76407,c_124132]) ).

tcf(c_125272,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11))
    | ( hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76408,c_124132]) ).

tcf(c_125273,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13))
    | ( hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76409,c_124132]) ).

tcf(c_125274,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14))
    | ( hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76410,c_124132]) ).

tcf(c_125275,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15))
    | ( hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76411,c_124132]) ).

tcf(c_125276,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16))
    | ( hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76412,c_124132]) ).

tcf(c_125277,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17))
    | ( hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76413,c_124132]) ).

tcf(c_125278,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18))
    | ( hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76414,c_124132]) ).

tcf(c_125280,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_77366,c_124132]) ).

tcf(c_125281,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78024,c_124132]) ).

tcf(c_125282,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,t)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,t)))
      | ( hAPP_int_int(times_times_int(sK27(X0,t)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78042,c_124132]) ).

tcf(c_125283,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,one_one_int)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,one_one_int)))
      | ( hAPP_int_int(times_times_int(sK27(X0,one_one_int)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78056,c_124132]) ).

tcf(c_125284,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)))
    | ( hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78203,c_124132]) ).

tcf(c_125285,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124132]) ).

tcf(c_125286,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124132]) ).

tcf(c_125287,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124132]) ).

tcf(c_125288,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124132]) ).

tcf(c_125289,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124132]) ).

tcf(c_125290,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124132]) ).

tcf(c_125291,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124132]) ).

tcf(c_125292,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124132]) ).

tcf(c_125293,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124132]) ).

tcf(c_125294,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124132]) ).

tcf(c_125295,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
    | ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88502,c_124132]) ).

tcf(c_125296,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88521,c_124132]) ).

tcf(c_125297,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88558,c_124132]) ).

tcf(c_125298,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124132]) ).

tcf(c_125299,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124132]) ).

tcf(c_125300,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124132]) ).

tcf(c_125301,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124132]) ).

tcf(c_125314,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125274,c_79239]) ).

tcf(c_125338,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),m))
    | ( hAPP_int_int(iPr_def_13,sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125266,c_59637]) ).

tcf(c_125342,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),one_one_int)) ),
    inference(ground_joinability,[status(thm)],[c_125262,c_76995]) ).

tcf(c_125366,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)) = sK30(iPr_def_19) )
      | ( hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19)) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125281,c_98749]) ).

tcf(c_125601,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_98014,c_124133]) ).

tcf(c_125602,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_98014,c_124133]) ).

tcf(c_125630,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124133]) ).

tcf(c_125631,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124133]) ).

tcf(c_125632,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124133]) ).

tcf(c_125633,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124133]) ).

tcf(c_125634,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124133]) ).

tcf(c_125635,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(X0),m)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124133]) ).

tcf(c_125636,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124133]) ).

tcf(c_125637,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124133]) ).

tcf(c_125638,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),m)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124133]) ).

tcf(c_125639,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124133]) ).

tcf(c_125643,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124133]) ).

tcf(c_125644,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124133]) ).

tcf(c_125645,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124133]) ).

tcf(c_125646,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124133]) ).

tcf(c_125668,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125632,c_90977]) ).

tcf(c_125672,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125631,c_90977]) ).

tcf(c_125778,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X1)),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_98014,c_124134]) ).

tcf(c_125779,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X0),m))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_98014,c_124134]) ).

tcf(c_125780,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),X1))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_106496,c_124134]) ).

tcf(c_125781,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(X1),m)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_106728,c_124134]) ).

tcf(c_125782,plain,
    ( ( hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_574,c_124134]) ).

tcf(c_125783,plain,
    ( ( hAPP_int_int(times_times_int(min),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(min),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),min) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76397,c_124134]) ).

tcf(c_125785,plain,
    ( ( hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(undefined_int(int)),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),undefined_int(int)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76395,c_124134]) ).

tcf(c_125786,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),twoSqu1241645765sum2sq(X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76399,c_124134]) ).

tcf(c_125787,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_nat_int(X0,X1)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_nat_int(X0,X1)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76401,c_124134]) ).

tcf(c_125788,plain,
    ( ( hAPP_int_int(times_times_int(m),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(m),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76402,c_124134]) ).

tcf(c_125789,plain,
    ( ( hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(s1),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),s1) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76403,c_124134]) ).

tcf(c_125790,plain,
    ( ( hAPP_int_int(times_times_int(s),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(s),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),s) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76404,c_124134]) ).

tcf(c_125791,plain,
    ( ( hAPP_int_int(times_times_int(t),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(t),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),t) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76405,c_124134]) ).

tcf(c_125792,plain,
    ( ( hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK9),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK9) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76406,c_124134]) ).

tcf(c_125793,plain,
    ( ( hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK10),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK10) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76407,c_124134]) ).

tcf(c_125794,plain,
    ( ( hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK11),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK11) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76408,c_124134]) ).

tcf(c_125795,plain,
    ( ( hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK13),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK13) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76409,c_124134]) ).

tcf(c_125796,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76410,c_124134]) ).

tcf(c_125797,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76411,c_124134]) ).

tcf(c_125798,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76412,c_124134]) ).

tcf(c_125799,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(iPr_def_17),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_17) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76413,c_124134]) ).

tcf(c_125800,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_76414,c_124134]) ).

tcf(c_125802,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_13,X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_13,X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_77366,c_124134]) ).

tcf(c_125803,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(iPr_def_12,X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(iPr_def_12,X0)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78024,c_124134]) ).

tcf(c_125804,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK27(X0,t)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK27(X0,t)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,t)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78042,c_124134]) ).

tcf(c_125805,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK27(X0,one_one_int)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK27(X0,one_one_int)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK27(X0,one_one_int)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78056,c_124134]) ).

tcf(c_125806,plain,
    ( ( hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK26(iPr_def_14)),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK26(iPr_def_14)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_78203,c_124134]) ).

tcf(c_125807,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79573,c_124134]) ).

tcf(c_125808,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79414,c_124134]) ).

tcf(c_125809,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79557,c_124134]) ).

tcf(c_125810,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79437,c_124134]) ).

tcf(c_125811,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_79918,c_124134]) ).

tcf(c_125812,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),m)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(plus_plus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_83504,c_124134]) ).

tcf(c_125813,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(m),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(m),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80664,c_124134]) ).

tcf(c_125814,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(sK30(iPr_def_19)),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80677,c_124134]) ).

tcf(c_125815,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),m)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),m)) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80692,c_124134]) ).

tcf(c_125816,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_80705,c_124134]) ).

tcf(c_125817,plain,
    ( ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88502,c_124134]) ).

tcf(c_125818,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88521,c_124134]) ).

tcf(c_125819,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),sK14(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19)),sK30(iPr_def_19),sK30(iPr_def_19))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_88558,c_124134]) ).

tcf(c_125820,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_96714,c_124134]) ).

tcf(c_125821,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19))),number_number_of_int(X0))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_99171,c_124134]) ).

tcf(c_125822,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(minus_minus_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_100498,c_124134]) ).

tcf(c_125823,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_int_int(plus_plus_int(m),sK30(iPr_def_19)))) != sK30(iPr_def_19) ) ),
    inference(superposition,[status(thm)],[c_103848,c_124134]) ).

tcf(c_125824,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_18),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_18) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125800,c_99786]) ).

tcf(c_125830,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_16),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_16) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125798,c_98811]) ).

tcf(c_125833,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_15),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_15) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125797,c_98789]) ).

tcf(c_125836,plain,
    ( ( hAPP_int_int(times_times_int(iPr_def_14),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),iPr_def_14) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125796,c_79216]) ).

tcf(c_125860,plain,
    ( ( hAPP_int_int(iPr_def_13,sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ~ is_int(hAPP_int_int(iPr_def_13,sK30(iPr_def_19)))
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125788,c_59637]) ).

tcf(c_125861,plain,
    ( ( hAPP_int_int(iPr_def_13,sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),m) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125860,c_77054]) ).

tcf(c_125864,plain,
    ( ( hAPP_int_int(times_times_int(min),sK30(iPr_def_19)) = sK30(iPr_def_19) )
    | ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),min) != sK30(iPr_def_19) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_125783,c_99798]) ).

tcf(c_125915,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),sK30(iPr_def_19))),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125809,c_90977]) ).

tcf(c_125919,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)) = sK30(iPr_def_19) )
      | ~ is_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),X0)),sK30(iPr_def_19)))
      | ( hAPP_int_int(times_times_int(number_number_of_int(X0)),hAPP_nat_int(power_power_int(sK30(iPr_def_19)),iPr_def_11)) != sK30(iPr_def_19) ) ),
    inference(light_normalisation,[status(thm)],[c_125808,c_90977]) ).

tcf(c_126077,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(pls)
      | ~ is_int(X0)
      | ( number267125858f_real(X0) != zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_568,c_247]) ).

tcf(c_126078,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X0))
      | ( hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(X0)) != number267125858f_real(X1) ) ),
    inference(superposition,[status(thm)],[c_408,c_247]) ).

tcf(c_126079,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(one_one_int)
      | ~ is_int(X0)
      | ( number267125858f_real(X0) != one_one_real ) ),
    inference(superposition,[status(thm)],[c_78124,c_247]) ).

tcf(c_126081,plain,
    ! [X0: $i] :
      ( ( X0 = one_one_int )
      | ~ is_int(X0)
      | ( number267125858f_real(X0) != one_one_real ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_126079,c_49]) ).

tcf(c_126085,plain,
    ! [X0: $i] :
      ( ( X0 = pls )
      | ~ is_int(X0)
      | ( number267125858f_real(X0) != zero_zero_real ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_126077,c_57]) ).

tcf(c_126089,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X0) = X1 )
      | ~ is_int(X1)
      | ~ is_int(hAPP_int_int(plus_plus_int(X0),X0))
      | ( number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)) != number267125858f_real(X1) ) ),
    inference(light_normalisation,[status(thm)],[c_126078,c_87834]) ).

tcf(c_126090,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(plus_plus_int(X0),X0) = X1 )
      | ~ is_int(X1)
      | ( number267125858f_real(hAPP_int_int(times_times_int(iPr_def_14),X0)) != number267125858f_real(X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_126089,c_79191]) ).

tcf(c_126105,plain,
    ! [X0: $i] :
      ( is_int(sK12(X0))
      | hBOOL(hAPP_int_bool(zprime,X0))
      | ~ is_int(X0)
      | ~ hBOOL(hAPP_int_bool(iPr_def_19,X0)) ),
    inference(light_normalisation,[status(thm)],[c_728,c_59643]) ).

tcf(c_126129,plain,
    ! [X0: $i,X1: $i] :
      ( is_int(sK30(zcong(X0,X1)))
      | ( X0 = X1 )
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(superposition,[status(thm)],[c_1563,c_828]) ).

tcf(c_126131,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_int_int(times_times_int(X0),pls) = hAPP_int_int(times_times_int(X1),pls) )
      | ~ is_int(hAPP_int_int(times_times_int(X1),pls))
      | ~ is_int(hAPP_int_int(times_times_int(X0),pls)) ),
    inference(superposition,[status(thm)],[c_833,c_828]) ).

tcf(c_126134,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(div_mod_int(X0),pls) = X0 )
      | ~ is_int(X0)
      | ~ is_int(hAPP_int_int(div_mod_int(X0),pls)) ),
    inference(superposition,[status(thm)],[c_1699,c_828]) ).

tcf(c_126138,plain,
    ( ( hAPP_int_int(times_times_int(pls),sK30(iPr_def_19)) = pls )
    | ~ is_int(pls)
    | ~ is_int(hAPP_int_int(times_times_int(pls),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_83491,c_828]) ).

tcf(c_126139,plain,
    ( ( hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls) = pls )
    | ~ is_int(pls)
    | ~ is_int(hAPP_int_int(times_times_int(sK30(iPr_def_19)),pls)) ),
    inference(superposition,[status(thm)],[c_84092,c_828]) ).

tcf(c_126141,plain,
    ( ( zfact(hAPP_int_int(minus_minus_int(pls),one_one_int)) = min )
    | ~ is_int(min)
    | ~ hBOOL(hAPP_int_bool(zprime,pls))
    | ~ is_int(zfact(hAPP_int_int(minus_minus_int(pls),one_one_int))) ),
    inference(superposition,[status(thm)],[c_110697,c_828]) ).

tcf(c_126149,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),pls) = pls )
      | ~ is_int(pls)
      | ~ is_int(hAPP_int_int(times_times_int(X0),pls)) ),
    inference(light_normalisation,[status(thm)],[c_126131,c_1001]) ).

tcf(c_126150,plain,
    ! [X0: $i] :
      ( ( hAPP_int_int(times_times_int(X0),pls) = pls )
      | ~ is_int(pls) ),
    inference(light_normalisation,[status(thm)],[c_126149,c_1001]) ).

tcf(c_126151,plain,
    ( ( one_one_int = min )
    | ~ is_int(min)
    | ~ is_int(one_one_int)
    | ~ hBOOL(hAPP_int_bool(zprime,pls)) ),
    inference(light_normalisation,[status(thm)],[c_126141,c_78632,c_78655]) ).

tcf(c_126152,plain,
    ( ( one_one_int = min )
    | ~ hBOOL(hAPP_int_bool(zprime,pls)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_126151,c_56,c_49]) ).

tcf(c_126155,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(min),X0) = min )
      | ( hAPP_nat_int(power_power_int(min),X0) = one_one_int ) ),
    inference(light_normalisation,[status(thm)],[c_934,c_76397]) ).

tcf(c_126170,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),X0) = one_one_int )
      | ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X0),X1)) = hAPP_nat_int(power_power_int(min),X1) ) ),
    inference(superposition,[status(thm)],[c_126155,c_676]) ).

tcf(c_126172,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,min),min))
      | ( hAPP_nat_int(power_power_int(min),X0) = one_one_int )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_126155,c_805]) ).

tcf(c_126173,plain,
    ( ( one_one_int = min )
    | ( hAPP_nat_int(power_power_int(min),zero_zero_nat) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_126155,c_784]) ).

tcf(c_126174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96622]) ).

tcf(c_126175,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96626]) ).

tcf(c_126176,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96474]) ).

tcf(c_126177,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96046]) ).

tcf(c_126178,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96050]) ).

tcf(c_126179,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95925]) ).

tcf(c_126180,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(times_times_int(min),hAPP_int_int(iPr_def_12,min)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_94503]) ).

tcf(c_126181,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(plus_plus_int(iPr_def_14),hAPP_int_int(plus_plus_int(iPr_def_14),min)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_83839]) ).

tcf(c_126182,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(plus_plus_int(hAPP_int_int(iPr_def_13,m)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_83271]) ).

tcf(c_126183,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_82919]) ).

tcf(c_126184,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(times_times_int(min),min) = min ) ),
    inference(superposition,[status(thm)],[c_126155,c_82861]) ).

tcf(c_126185,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),min)) ),
    inference(superposition,[status(thm)],[c_126155,c_81992]) ).

tcf(c_126186,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(times_times_int(iPr_def_14),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_79175]) ).

tcf(c_126187,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),min))
    | ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_126155,c_79141]) ).

tcf(c_126188,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min))
    | ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int ) ),
    inference(superposition,[status(thm)],[c_126155,c_78970]) ).

tcf(c_126189,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( min != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_78501]) ).

tcf(c_126190,plain,
    ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
    | ( hAPP_int_int(iPr_def_12,min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_76355]) ).

tcf(c_126191,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_59645]) ).

tcf(c_126192,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_82918]) ).

tcf(c_126193,plain,
    ! [X0: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_59645]) ).

tcf(c_126195,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96174]) ).

tcf(c_126196,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96088]) ).

tcf(c_126198,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96015]) ).

tcf(c_126200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96605]) ).

tcf(c_126201,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96465]) ).

tcf(c_126204,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96019]) ).

tcf(c_126205,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95916]) ).

tcf(c_126207,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95923]) ).

tcf(c_126208,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96510]) ).

tcf(c_126209,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96015]) ).

tcf(c_126210,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95923]) ).

tcf(c_126211,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96169]) ).

tcf(c_126212,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95924]) ).

tcf(c_126213,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_95925]) ).

tcf(c_126214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96521]) ).

tcf(c_126215,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_int_int(times_times_int(X0),X0)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96084]) ).

tcf(c_126216,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(times_times_int(iPr_def_14),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96062]) ).

tcf(c_126217,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96011]) ).

tcf(c_126218,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96169]) ).

tcf(c_126219,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96011]) ).

tcf(c_126220,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96174]) ).

tcf(c_126221,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96019]) ).

tcf(c_126222,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96134]) ).

tcf(c_126223,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96046]) ).

tcf(c_126224,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96138]) ).

tcf(c_126225,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96050]) ).

tcf(c_126226,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(iPr_def_11),X2)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96465]) ).

tcf(c_126227,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(iPr_def_11),X2))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96474]) ).

tcf(c_126228,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96506]) ).

tcf(c_126229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96506]) ).

tcf(c_126230,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(min),hAPP_nat_int(power_power_int(X0),iPr_def_11)) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96510]) ).

tcf(c_126231,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),iPr_def_11))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96605]) ).

tcf(c_126232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),iPr_def_11)))),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96521]) ).

tcf(c_126233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X2),hAPP_nat_nat(times_times_nat(X3),iPr_def_11)))) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96622]) ).

tcf(c_126234,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP_nat_int(power_power_int(min),hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X1),iPr_def_11)),iPr_def_11)) = one_one_int )
      | ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),iPr_def_11)),min) != iPr_def_18 ) ),
    inference(superposition,[status(thm)],[c_126155,c_96626]) ).

tcf(c_126242,plain,
    ( ( one_one_int = min )
    | ( hAPP_nat_int(power_power_int(min),iPr_def_11) = one_one_int ) ),
    inference(light_normalisation,[status(thm)],[c_126184,c_79464]) ).

tcf(c_126462,plain,
    ! [X0: $i] : hBOOL(hAPP_int_bool(zcong(sK9,hAPP_int_int(times_times_int(sK9),X0)),sK9)),
    inference(superposition,[status(thm)],[c_253,c_78309]) ).

tcf(c_126464,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP_int_bool(zcong(sK9,hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),sK9))),sK9)),
    inference(superposition,[status(thm)],[c_252,c_78309]) ).

tcf(c_126465,plain,
    hBOOL(hAPP_int_bool(zcong(sK9,pls),sK9)),
    inference(superposition,[status(thm)],[c_1004,c_78309]) ).

tcf(c_126466,plain,
    hBOOL(hAPP_int_bool(zcong(sK9,hAPP_int_int(plus_plus_int(sK9),sK9)),sK9)),
    inference(superposition,[status(thm)],[c_79150,c_78309]) ).

tcf(c_126467,plain,
    hBOOL(hAPP_int_bool(zcong(sK9,hAPP_int_int(iPr_def_13,sK9)),sK9)),
    inference(superposition,[status(thm)],[c_59637,c_78309]) ).

tcf(c_126468,plain,
    ! [X0: $i] : hBOOL(member_int(sK9,zcong(sK9,hAPP_int_int(times_times_int(X0),sK9)))),
    inference(superposition,[status(thm)],[c_78309,c_226]) ).

tcf(c_126469,plain,
    ! [X0: $i] :
      ( is_int(sK14(sK9,hAPP_int_int(times_times_int(X0),sK9),sK9))
      | ~ is_int(hAPP_int_int(times_times_int(X0),sK9)) ),
    inference(superposition,[status(thm)],[c_78309,c_852]) ).

tcf(c_126504,plain,
    hBOOL(member_int(sK9,zcong(sK9,hAPP_int_int(iPr_def_13,sK9)))),
    inference(superposition,[status(thm)],[c_126467,c_226]) ).

tcf(c_126505,plain,
    ( is_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9))
    | ~ is_int(hAPP_int_int(iPr_def_13,sK9)) ),
    inference(superposition,[status(thm)],[c_126467,c_852]) ).

tcf(c_126506,plain,
    hBOOL(hAPP_int_bool(zcong(hAPP_int_int(iPr_def_13,sK9),sK9),sK9)),
    inference(superposition,[status(thm)],[c_126467,c_814]) ).

tcf(c_126507,plain,
    is_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),
    inference(forward_subsumption_resolution,[status(thm)],[c_126505,c_77054]) ).

tcf(c_126527,plain,
    ! [X0: $i] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),X0)) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_46106]) ).

tcf(c_126528,plain,
    ! [X0: $i] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9))),X0) = pls,
    inference(superposition,[status(thm)],[c_126507,c_46104]) ).

tcf(c_126529,plain,
    hAPP_int_int(minus_minus_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),pls) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_880]) ).

tcf(c_126530,plain,
    hAPP_nat_int(power_power_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),one_one_nat) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_608]) ).

tcf(c_126531,plain,
    hAPP_int_int(plus_plus_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),pls) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_524]) ).

tcf(c_126532,plain,
    hAPP_int_int(plus_plus_int(pls),sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_523]) ).

tcf(c_126533,plain,
    hAPP_int_int(times_times_int(one_one_int),sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_347]) ).

tcf(c_126534,plain,
    hAPP_int_int(times_times_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)),one_one_int) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_346]) ).

tcf(c_126535,plain,
    number_number_of_int(sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9)) = sK14(sK9,hAPP_int_int(iPr_def_13,sK9),sK9),
    inference(superposition,[status(thm)],[c_126507,c_254]) ).

tcf(c_126559,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ( hAPP_nat_real(power_power_real(X0),X1) = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ),
    inference(superposition,[status(thm)],[c_527,c_969]) ).

tcf(c_126562,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
      | ( number267125858f_real(X0) = zero_zero_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_626,c_969]) ).

tcf(c_126563,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
      | ( number267125858f_real(X0) = zero_zero_real )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
    inference(superposition,[status(thm)],[c_630,c_969]) ).

tcf(c_126564,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X0),X1)))
      | ( hAPP_nat_real(power_power_real(X0),X1) = one_one_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X0)) ),
    inference(superposition,[status(thm)],[c_698,c_969]) ).

tcf(c_126565,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(X0),X1)),zero_zero_real))
      | ( hAPP_real_real(minus_minus_real(X0),X1) = zero_zero_real )
      | ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
    inference(superposition,[status(thm)],[c_956,c_969]) ).

tcf(c_126569,plain,
    ! [X0: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0)))
      | ( hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),X0) = one_one_real ) ),
    inference(superposition,[status(thm)],[c_14104,c_969]) ).

tcf(c_126572,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1))))
      | ( hAPP_nat_real(power_power_real(X0),hAPP_nat_nat(times_times_nat(iPr_def_11),X1)) = zero_zero_real ) ),
    inference(superposition,[status(thm)],[c_89096,c_969]) ).

tcf(c_126573,plain,
    ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(sK30(iPr_def_19))),one_one_real))
    | ( number267125858f_real(sK30(iPr_def_19)) = one_one_real )
    | ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,one_one_int),sK30(iPr_def_19))) ),
    inference(superposition,[status(thm)],[c_89285,c_969]) ).

fof(f2208,definition,
    ! [X0,X2,X1] :
      ( sP2(X0,X2,X1)
    <=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).

fof(f2209,definition,
    ! [X0,X2,X1] :
      ( sP3(X0,X2,X1)
    <=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
        | ! [X3,X4] :
            ( ~ is_int(X4)
            | ~ is_int(X3)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X3)),X4) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),X2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
            | hBOOL(hAPP_int_bool(X0,X4)) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).

fof(f2210,plain,
    ! [X0,X1,X2] :
      ( ~ is_int(X2)
      | ~ is_int(X1)
      | ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(div_mod_int(X1),X2)))
      <=> ( sP2(X0,X2,X1)
          & sP3(X0,X2,X1)
          & ( zero_zero_int != X2
            | hBOOL(hAPP_int_bool(X0,X1)) ) ) ) ),
    inference(definition_folding,[],[f2172,f2209,f2208]) ).

fof(f2211,definition,
    ! [X1,X0,X2] :
      ( sP4(X1,X0,X2)
    <=> ( ( zero_zero_nat = X2
          | ! [X3,X4] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) != X1
              | hBOOL(hAPP_nat_bool(X0,X4)) ) )
        & ( zero_zero_nat != X2
          | hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).

fof(f2212,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(div_mod_nat(X1),X2)))
    <=> sP4(X1,X0,X2) ),
    inference(definition_folding,[],[f2198,f2211]) ).

fof(f2587,plain,
    ! [X0,X2,X1] :
      ( ( ~ sP2(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
          & ? [X5,X6] :
              ( is_int(X6)
              & is_int(X5)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) = X1
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
              & ~ hBOOL(hAPP_int_bool(X0,X6)) ) )
        | sP2(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f2208]) ).

fof(f2588,plain,
    ! [X0,X2,X1] :
      ( ( ~ sP2(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) != X1
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
          & ? [X5,X6] :
              ( is_int(X6)
              & is_int(X5)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X2),X5)),X6) = X1
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X6))
              & ~ hBOOL(hAPP_int_bool(X0,X6)) ) )
        | sP2(X0,X2,X1) ) ),
    inference(flattening,[],[f2587]) ).

fof(f2589,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP2(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
          & ? [X3,X4] :
              ( is_int(X4)
              & is_int(X3)
              & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X3)),X4) = X2
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),zero_zero_int))
              & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X4))
              & ~ hBOOL(hAPP_int_bool(X0,X4)) ) )
        | sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f2588]) ).

fof(f2590,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP2(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
        | ! [X5,X6] :
            ( ~ is_int(X6)
            | ~ is_int(X5)
            | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X6))
            | hBOOL(hAPP_int_bool(X0,X6)) ) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
          & is_int(sK41(X0,X1,X2))
          & is_int(sK40(X0,X1,X2))
          & hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),sK40(X0,X1,X2))),sK41(X0,X1,X2)) = X2
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),zero_zero_int))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sK41(X0,X1,X2)))
          & ~ hBOOL(hAPP_int_bool(X0,sK41(X0,X1,X2))) )
        | sP2(X0,X1,X2) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X3,sK40(X0,X1,X2)),skolemize(X4,sK41(X0,X1,X2))],[f2589]) ).

fof(f2600,plain,
    ! [X1,X0,X2] :
      ( ( ~ sP4(X1,X0,X2)
        | ( ( zero_zero_nat = X2
            | ! [X3,X4] :
                ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
                | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) != X1
                | hBOOL(hAPP_nat_bool(X0,X4)) ) )
          & ( zero_zero_nat != X2
            | hBOOL(hAPP_nat_bool(X0,X1)) ) ) )
      & ( ( zero_zero_nat != X2
          & ? [X3,X4] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              & hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) = X1
              & ~ hBOOL(hAPP_nat_bool(X0,X4)) ) )
        | ( zero_zero_nat = X2
          & ~ hBOOL(hAPP_nat_bool(X0,X1)) )
        | sP4(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f2211]) ).

fof(f2601,plain,
    ! [X1,X0,X2] :
      ( ( ~ sP4(X1,X0,X2)
        | ( ( zero_zero_nat = X2
            | ! [X3,X4] :
                ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
                | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) != X1
                | hBOOL(hAPP_nat_bool(X0,X4)) ) )
          & ( zero_zero_nat != X2
            | hBOOL(hAPP_nat_bool(X0,X1)) ) ) )
      & ( ( zero_zero_nat != X2
          & ? [X3,X4] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              & hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) = X1
              & ~ hBOOL(hAPP_nat_bool(X0,X4)) ) )
        | ( zero_zero_nat = X2
          & ~ hBOOL(hAPP_nat_bool(X0,X1)) )
        | sP4(X1,X0,X2) ) ),
    inference(flattening,[],[f2600]) ).

fof(f2602,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP4(X0,X1,X2)
        | ( ( zero_zero_nat = X2
            | ! [X5,X6] :
                ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6),X2))
                | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X5)),X6) != X0
                | hBOOL(hAPP_nat_bool(X1,X6)) ) )
          & ( zero_zero_nat != X2
            | hBOOL(hAPP_nat_bool(X1,X0)) ) ) )
      & ( ( zero_zero_nat != X2
          & ? [X3,X4] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
              & hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X3)),X4) = X0
              & ~ hBOOL(hAPP_nat_bool(X1,X4)) ) )
        | ( zero_zero_nat = X2
          & ~ hBOOL(hAPP_nat_bool(X1,X0)) )
        | sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f2601]) ).

fof(f2603,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP4(X0,X1,X2)
        | ( ( zero_zero_nat = X2
            | ! [X5,X6] :
                ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6),X2))
                | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X5)),X6) != X0
                | hBOOL(hAPP_nat_bool(X1,X6)) ) )
          & ( zero_zero_nat != X2
            | hBOOL(hAPP_nat_bool(X1,X0)) ) ) )
      & ( ( zero_zero_nat != X2
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X0,X1,X2)),X2))
          & hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),sK44(X0,X1,X2))),sK45(X0,X1,X2)) = X0
          & ~ hBOOL(hAPP_nat_bool(X1,sK45(X0,X1,X2))) )
        | ( zero_zero_nat = X2
          & ~ hBOOL(hAPP_nat_bool(X1,X0)) )
        | sP4(X0,X1,X2) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44,sK45]),skolemize(X3,sK44(X0,X1,X2)),skolemize(X4,sK45(X0,X1,X2))],[f2602]) ).

fof(f4276,plain,
    ! [X2,X0,X1,X6,X5] :
      ( ~ sP2(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4277,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4278,plain,
    ! [X2,X0,X1] :
      ( is_int(sK41(X0,X1,X2))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4279,plain,
    ! [X2,X0,X1] :
      ( is_int(sK40(X0,X1,X2))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4280,plain,
    ! [X2,X0,X1] :
      ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),sK40(X0,X1,X2))),sK41(X0,X1,X2)) = X2
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4281,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),zero_zero_int))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4282,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sK41(X0,X1,X2)))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4283,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_int_bool(X0,sK41(X0,X1,X2)))
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2590]) ).

fof(f4325,plain,
    ! [X2,X0,X1,X6,X5] :
      ( ~ sP4(X0,X1,X2)
      | zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6),X2))
      | hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X5)),X6) != X0
      | hBOOL(hAPP_nat_bool(X1,X6)) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4326,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X0,X1,X2)
      | zero_zero_nat != X2
      | hBOOL(hAPP_nat_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4328,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X0,X1,X2)),X2))
      | zero_zero_nat = X2
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4329,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),sK44(X0,X1,X2))),sK45(X0,X1,X2)) = X0
      | zero_zero_nat = X2
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4330,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X1,sK45(X0,X1,X2)))
      | zero_zero_nat = X2
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4331,plain,
    ! [X2,X0,X1] :
      ( zero_zero_nat != X2
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4332,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4333,plain,
    ! [X2,X0,X1] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),sK44(X0,X1,X2))),sK45(X0,X1,X2)) = X0
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4334,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X1,sK45(X0,X1,X2)))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f2603]) ).

fof(f4911,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),pls))
      | sP2(X0,X1,X2) ),
    inference(definition_unfolding,[],[f4281,f3091]) ).

fof(f4912,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | sP2(X0,X1,X2) ),
    inference(definition_unfolding,[],[f4277,f3091]) ).

fof(f4913,plain,
    ! [X2,X0,X1,X6,X5] :
      ( ~ sP2(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6) != X2
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(definition_unfolding,[],[f4276,f3091,f3091]) ).

fof(f5127,plain,
    ! [X0,X1,X6,X5] :
      ( ~ sP2(X0,X1,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X5)),X6))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ is_int(X6)
      | ~ is_int(X5)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X6))
      | hBOOL(hAPP_int_bool(X0,X6)) ),
    inference(equality_resolution,[],[f4913]) ).

fof(f5134,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_nat_bool(X1,X0))
      | sP4(X0,X1,zero_zero_nat) ),
    inference(equality_resolution,[],[f4331]) ).

fof(f5136,plain,
    ! [X0,X1] :
      ( ~ sP4(X0,X1,zero_zero_nat)
      | hBOOL(hAPP_nat_bool(X1,X0)) ),
    inference(equality_resolution,[],[f4326]) ).

fof(f5137,plain,
    ! [X2,X1,X6,X5] :
      ( ~ sP4(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),X5)),X6),X1,X2)
      | zero_zero_nat = X2
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6),X2))
      | hBOOL(hAPP_nat_bool(X1,X6)) ),
    inference(equality_resolution,[],[f4325]) ).

tcf(c_1655,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,sK41(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f4283]) ).

tcf(c_1656,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK41(X1,X0,X2))) ),
    inference(cnf_transformation,[],[f4282]) ).

tcf(c_1657,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),pls)) ),
    inference(cnf_transformation,[],[f4911]) ).

tcf(c_1658,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK40(X1,X0,X2))),sK41(X1,X0,X2)) = X2 ) ),
    inference(cnf_transformation,[],[f4280]) ).

tcf(c_1659,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | is_int(sK40(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f4279]) ).

tcf(c_1660,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | is_int(sK41(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f4278]) ).

tcf(c_1661,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f4912]) ).

tcf(c_1662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_int_bool(X0,X3))
      | ~ is_int(X3)
      | ~ is_int(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
      | ~ sP2(X0,X1,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),X3)) ),
    inference(cnf_transformation,[],[f5127]) ).

tcf(c_1702,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,X1))
      | ~ hBOOL(hAPP_nat_bool(X0,sK45(X1,X0,X2))) ),
    inference(cnf_transformation,[],[f4334]) ).

tcf(c_1703,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X2),sK44(X1,X0,X2))),sK45(X1,X0,X2)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4333]) ).

tcf(c_1704,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X1,X0,X2)),X2))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f4332]) ).

tcf(c_1705,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,X0,zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f5134]) ).

tcf(c_1706,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | ( X2 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(X0,sK45(X1,X0,X2))) ),
    inference(cnf_transformation,[],[f4330]) ).

tcf(c_1707,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X2,X0)
      | ( X0 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),sK44(X1,X2,X0))),sK45(X1,X2,X0)) = X1 ) ),
    inference(cnf_transformation,[],[f4329]) ).

tcf(c_1708,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X2,X0)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X1,X2,X0)),X0))
      | ( X0 = zero_zero_nat ) ),
    inference(cnf_transformation,[],[f4328]) ).

tcf(c_1709,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ~ sP4(X0,X1,zero_zero_nat) ),
    inference(cnf_transformation,[],[f5136]) ).

tcf(c_1710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP_nat_bool(X3,X2))
      | ( X0 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | ~ sP4(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2),X3,X0) ),
    inference(cnf_transformation,[],[f5137]) ).

tcf(c_3487,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),pls))
      | sP2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_1657]) ).

tcf(c_3488,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK41(X0,X1,X2)),pls)) ),
    inference(renaming,[status(thm)],[c_3487]) ).

tcf(c_3551,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK40(X1,X0,X2))),sK41(X1,X0,X2)) = X2 )
      | sP2(X1,X0,X2) ),
    inference(prop_impl_just,[status(thm)],[c_1658]) ).

tcf(c_3552,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),sK40(X1,X0,X2))),sK41(X1,X0,X2)) = X2 ) ),
    inference(renaming,[status(thm)],[c_3551]) ).

tcf(c_11418,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK41(X0,X1,X2))) ),
    inference(demodulation,[status(thm)],[c_3488,c_1720]) ).

tcf(c_12956,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK41(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK40(X0,X1,X2))) = X2 ) ),
    inference(demodulation,[status(thm)],[c_3552,c_241]) ).

tcf(c_13941,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,X1,X2)
      | ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(sK45(X0,X1,X2)),hAPP_nat_nat(times_times_nat(X2),sK44(X0,X1,X2))) = X0 ) ),
    inference(demodulation,[status(thm)],[c_1707,c_242]) ).

tcf(c_14078,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,X0,X2)
      | ( hAPP_nat_nat(plus_plus_nat(sK45(X1,X0,X2)),hAPP_nat_nat(times_times_nat(X2),sK44(X1,X0,X2))) = X1 )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_1703,c_242]) ).

tcf(c_46646,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK41(X0,X1,X2)))
      | sP2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_11418]) ).

tcf(c_46647,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),sK41(X0,X1,X2))) ),
    inference(renaming,[status(thm)],[c_46646]) ).

tcf(c_46648,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hAPP_int_int(plus_plus_int(sK41(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK40(X0,X1,X2))) = X2 )
      | sP2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_12956]) ).

tcf(c_46649,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK41(X0,X1,X2)),hAPP_int_int(times_times_int(X1),sK40(X0,X1,X2))) = X2 ) ),
    inference(renaming,[status(thm)],[c_46648]) ).

tcf(c_76635,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( number_number_of_int(sK40(X0,X1,X2)) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_254]) ).

tcf(c_76643,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( number_number_of_int(sK41(X0,X1,X2)) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_254]) ).

tcf(c_76672,plain,
    ! [X0: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1330,c_1705]) ).

tcf(c_76673,plain,
    ! [X0: $i] : sP4(zero_zero_nat,hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1591,c_1705]) ).

tcf(c_76674,plain,
    ! [X0: $i] : sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1282,c_1705]) ).

tcf(c_76675,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),X1),hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1044,c_1705]) ).

tcf(c_76676,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),X1),hAPP_n1699378549t_bool(dvd_dvd_nat,X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1041,c_1705]) ).

tcf(c_76677,plain,
    ! [X0: $i] : sP4(X0,hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1594,c_1705]) ).

tcf(c_76678,plain,
    ! [X0: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1365,c_1705]) ).

tcf(c_76679,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1299,c_1705]) ).

tcf(c_76680,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1373,c_1705]) ).

tcf(c_76681,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1375,c_1705]) ).

tcf(c_76682,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),X0),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1409,c_1705]) ).

tcf(c_76683,plain,
    ! [X0: $i,X1: $i] : sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1694,c_1705]) ).

tcf(c_76684,plain,
    sP4(one_one_nat,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_11147,c_1705]) ).

tcf(c_76685,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(iPr_def_10,X0),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76584,c_1705]) ).

tcf(c_76686,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(iPr_def_10,X0),hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76588,c_1705]) ).

tcf(c_76687,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76648,c_1705]) ).

tcf(c_76730,plain,
    sP4(one_one_nat,hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76367,c_76685]) ).

tcf(c_76733,plain,
    sP4(one_one_nat,hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76367,c_76686]) ).

tcf(c_76736,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_76735,c_1705]) ).

tcf(c_76815,plain,
    sP4(zero_zero_nat,hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1336,c_76675]) ).

tcf(c_76823,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(minus_minus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X2),X1))),zero_zero_nat),
    inference(superposition,[status(thm)],[c_11972,c_76679]) ).

tcf(c_76824,plain,
    sP4(zero_zero_nat,hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1244,c_76679]) ).

tcf(c_76922,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(sK40(X0,X1,X2)),one_one_int) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_346]) ).

tcf(c_76923,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(sK41(X0,X1,X2)),one_one_int) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_346]) ).

tcf(c_77083,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(one_one_int),sK40(X0,X1,X2)) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_347]) ).

tcf(c_77084,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(times_times_int(one_one_int),sK41(X0,X1,X2)) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_347]) ).

tcf(c_77158,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(pls),sK40(X0,X1,X2)) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_523]) ).

tcf(c_77159,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(pls),sK41(X0,X1,X2)) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_523]) ).

tcf(c_77233,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK40(X0,X1,X2)),pls) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_524]) ).

tcf(c_77234,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(plus_plus_int(sK41(X0,X1,X2)),pls) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_524]) ).

tcf(c_77309,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_nat_int(power_power_int(sK40(X0,X1,X2)),one_one_nat) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_608]) ).

tcf(c_77310,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_nat_int(power_power_int(sK41(X0,X1,X2)),one_one_nat) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_608]) ).

tcf(c_77424,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(minus_minus_int(sK40(X0,X1,X2)),pls) = sK40(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1659,c_880]) ).

tcf(c_77425,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ( hAPP_int_int(minus_minus_int(sK41(X0,X1,X2)),pls) = sK41(X0,X1,X2) ) ),
    inference(superposition,[status(thm)],[c_1660,c_880]) ).

tcf(c_77587,plain,
    ! [X0: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)
      | ( X0 = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1705]) ).

tcf(c_77657,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_int_bool(iPr_def_19,pls))
      | sP2(X0,one_one_int,X1) ),
    inference(superposition,[status(thm)],[c_59643,c_1661]) ).

tcf(c_77659,plain,
    ! [X0: $i,X1: $i] : sP2(X0,pls,X1),
    inference(superposition,[status(thm)],[c_1661,c_571]) ).

tcf(c_77660,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | hBOOL(member_int(pls,hAPP_i1948725293t_bool(ord_less_int,X0))) ),
    inference(superposition,[status(thm)],[c_1661,c_226]) ).

tcf(c_78123,plain,
    ! [X0: $i,X1: $i] : sP2(X0,one_one_int,X1),
    inference(forward_subsumption_resolution,[status(thm)],[c_77657,c_77847]) ).

tcf(c_78378,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1684,c_76683]) ).

tcf(c_78468,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1295,c_1705]) ).

tcf(c_78564,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X0),X0)),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1408,c_1705]) ).

tcf(c_78799,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_int(sK30(X0))
      | sP2(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_1563,c_1655]) ).

tcf(c_78800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1,X2)
      | sP3(X0,sK41(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_46418,c_1655]) ).

tcf(c_78801,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP2(zcong(X0,X0),X1,X2),
    inference(superposition,[status(thm)],[c_815,c_1655]) ).

tcf(c_78802,plain,
    ! [X0: $i,X1: $i] : sP2(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),X0,X1),
    inference(superposition,[status(thm)],[c_1051,c_1655]) ).

tcf(c_78822,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(div_mod_nat(X0),X2),X1,zero_zero_nat)
      | ~ sP4(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_1711,c_1705]) ).

tcf(c_78943,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1720,c_1661]) ).

tcf(c_78979,plain,
    ! [X0: $i,X1: $i] : sP2(cOMBC_int_int_bool(dvd_dvd_int,pls),X0,X1),
    inference(superposition,[status(thm)],[c_78946,c_1655]) ).

tcf(c_79356,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(times_times_nat(iPr_def_11),X0),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_79342,c_76680]) ).

tcf(c_81171,plain,
    ! [X0: $i,X1: $i] : sP2(hAPP_i1948725293t_bool(dvd_dvd_int,min),X0,X1),
    inference(superposition,[status(thm)],[c_81106,c_1655]) ).

tcf(c_81399,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | ~ hBOOL(member_int(pls,d22set(X0))) ),
    inference(superposition,[status(thm)],[c_1661,c_1579]) ).

tcf(c_81952,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ~ hBOOL(member_int(sK41(X0,X1,X2),d22set(X1))) ),
    inference(superposition,[status(thm)],[c_1656,c_1579]) ).

tcf(c_81953,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | hBOOL(member_int(sK41(X0,X1,X2),hAPP_i1948725293t_bool(ord_less_int,X1))) ),
    inference(superposition,[status(thm)],[c_1656,c_226]) ).

tcf(c_81955,plain,
    ! [X0: $i,X1: $i] : sP2(hAPP_i1948725293t_bool(ord_less_int,X0),X0,X1),
    inference(superposition,[status(thm)],[c_1656,c_1655]) ).

tcf(c_82320,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(power_power_nat(X0),iPr_def_11),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_82316,c_76682]) ).

tcf(c_82325,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(power_power_nat(X0),iPr_def_11),hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_82316,c_76676]) ).

tcf(c_82976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X1,X2,X3)
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK40(X1,X2,X3))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_1659,c_46104]) ).

tcf(c_82977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X1,X2,X3)
      | ( hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(X0),sK41(X1,X2,X3))),X0) = pls ) ),
    inference(superposition,[status(thm)],[c_1660,c_46104]) ).

tcf(c_83609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X1,X2,X3)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK40(X1,X2,X3)),X0)) = sK40(X1,X2,X3) ) ),
    inference(superposition,[status(thm)],[c_1659,c_46106]) ).

tcf(c_83610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X1,X2,X3)
      | ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(minus_minus_int(sK41(X1,X2,X3)),X0)) = sK41(X1,X2,X3) ) ),
    inference(superposition,[status(thm)],[c_1660,c_46106]) ).

tcf(c_84077,plain,
    ! [X0: $i] : sP2(iPr_def_19,one_one_int,X0),
    inference(superposition,[status(thm)],[c_59643,c_81955]) ).

tcf(c_85853,plain,
    ! [X0: $i] :
      ( sP4(number_number_of_nat(X0),hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(superposition,[status(thm)],[c_45950,c_1705]) ).

tcf(c_86372,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X1,X0,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(superposition,[status(thm)],[c_1661,c_46112]) ).

tcf(c_86377,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK41(X0,X1,X2)),X1)) ),
    inference(superposition,[status(thm)],[c_1656,c_46112]) ).

tcf(c_88100,plain,
    ! [X0: $i,X1: $i] : sP2(X0,t,X1),
    inference(superposition,[status(thm)],[c_1661,c_86382]) ).

tcf(c_88773,plain,
    ! [X0: $i,X1: $i] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | sP4(sK35(X1,X0),X0,zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1577,c_1705]) ).

tcf(c_88794,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(sK36(X0,X1),hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1582,c_1705]) ).

tcf(c_90309,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(number_number_of_nat(X0),hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),zero_zero_nat)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(superposition,[status(thm)],[c_131,c_1705]) ).

tcf(c_90311,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(number_number_of_nat(X0),hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),zero_zero_nat)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X0)),number_number_of_nat(X1))) ),
    inference(superposition,[status(thm)],[c_131,c_1705]) ).

tcf(c_90638,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP2(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1,X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),sK41(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(iPr_def_12,X0)),X1,X2))) ),
    inference(superposition,[status(thm)],[c_90614,c_1655]) ).

tcf(c_91259,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X1)),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_218,c_76682]) ).

tcf(c_91266,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X2)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_218,c_76676]) ).

tcf(c_91267,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_n1699378549t_bool(dvd_dvd_nat,X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_218,c_76675]) ).

tcf(c_94032,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_94015,c_76681]) ).

tcf(c_94038,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(iPr_def_10,X0)),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_94015,c_76680]) ).

tcf(c_96362,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(hAPP_nat_nat(power_power_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X0)) ),
    inference(superposition,[status(thm)],[c_699,c_1705]) ).

tcf(c_96430,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(hAPP_nat_nat(power_power_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_741,c_1705]) ).

tcf(c_97206,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(hAPP_nat_nat(power_power_nat(X1),X0),hAPP_n1699378549t_bool(dvd_dvd_nat,X1),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_803,c_1705]) ).

tcf(c_97276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X2,X0,X3)
      | ( hAPP_nat_nat(times_times_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1661,c_820]) ).

tcf(c_97286,plain,
    ! [X0: $i,X1: $i] : sP2(X0,iPr_def_15,X1),
    inference(superposition,[status(thm)],[c_1661,c_95997]) ).

tcf(c_97289,plain,
    ! [X0: $i,X1: $i] : sP2(X0,iPr_def_14,X1),
    inference(superposition,[status(thm)],[c_1661,c_96001]) ).

tcf(c_101537,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(times_times_nat(X2),X1),hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1035,c_1705]) ).

tcf(c_101747,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(times_times_nat(X1),X2),hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1038,c_1705]) ).

tcf(c_102886,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1705]) ).

tcf(c_102898,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1705]) ).

tcf(c_103044,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1262,c_1705]) ).

tcf(c_103096,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat),
    inference(superposition,[status(thm)],[c_102905,c_1705]) ).

tcf(c_104257,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1285,c_76681]) ).

tcf(c_104264,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X2)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1285,c_76680]) ).

tcf(c_104376,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1286,c_76681]) ).

tcf(c_104383,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1286,c_76680]) ).

tcf(c_104455,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(minus_minus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(plus_plus_nat(X1),X2))),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1291,c_76679]) ).

tcf(c_104550,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1292,c_76679]) ).

tcf(c_104628,plain,
    ! [X0: $i] : sP4(hAPP_nat_nat(iPr_def_10,X0),hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat),
    inference(superposition,[status(thm)],[c_102906,c_1705]) ).

tcf(c_105069,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(X0),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1293,c_76679]) ).

tcf(c_105119,plain,
    ! [X0: $i,X1: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),hAPP_nat_nat(times_times_nat(X0),X1))),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1308,c_76682]) ).

tcf(c_105130,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_n1699378549t_bool(dvd_dvd_nat,X2),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1308,c_76676]) ).

tcf(c_105131,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(times_times_nat(X0),hAPP_nat_nat(times_times_nat(X1),X2)),hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1308,c_76675]) ).

tcf(c_105242,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(hAPP_nat_nat(minus_minus_nat(X1),X0),hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1319,c_1705]) ).

tcf(c_106208,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(X1),X2),hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1347,c_1705]) ).

tcf(c_106256,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(X2),X1),hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1348,c_1705]) ).

tcf(c_107537,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)
      | ( hAPP_nat_nat(plus_plus_nat(X0),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X1 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1705]) ).

tcf(c_107586,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(X1),X0),hAPP_n1699378549t_bool(dvd_dvd_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1369,c_1705]) ).

tcf(c_107727,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_nat,sK18(one_one_nat,iPr_def_11)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_107667,c_104628]) ).

tcf(c_107737,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_eq_nat,sK18(one_one_nat,iPr_def_11)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_107667,c_76685]) ).

tcf(c_108482,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(X1),X2),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1379,c_1705]) ).

tcf(c_108520,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(hAPP_nat_nat(plus_plus_nat(X2),X1),hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(superposition,[status(thm)],[c_1380,c_1705]) ).

tcf(c_110853,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X1),X0)),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1682,c_1705]) ).

tcf(c_110864,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_nat,sK36(one_one_nat,iPr_def_11)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_110749,c_104628]) ).

tcf(c_110874,plain,
    sP4(iPr_def_11,hAPP_n1699378549t_bool(ord_less_eq_nat,sK36(one_one_nat,iPr_def_11)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_110749,c_76685]) ).

tcf(c_112458,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(X1),X0)),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(superposition,[status(thm)],[c_1683,c_1705]) ).

tcf(c_112491,plain,
    ! [X0: $i,X1: $i,X2: $i] : sP4(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X0),X1)),X2),hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(X2),X1)),zero_zero_nat),
    inference(superposition,[status(thm)],[c_1689,c_76683]) ).

tcf(c_112536,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)
      | ( X0 = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1330,c_1706]) ).

tcf(c_112537,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)
      | ( X1 = zero_zero_nat )
      | ( sK45(X0,hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1) = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1316,c_1706]) ).

tcf(c_112539,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),X0)
      | ( X0 = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1594,c_1706]) ).

tcf(c_112540,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2)
      | ( X2 = zero_zero_nat )
      | ( hAPP_nat_nat(plus_plus_nat(sK45(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),sK45(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2))) = X1 ) ),
    inference(superposition,[status(thm)],[c_1353,c_1706]) ).

tcf(c_112541,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK45(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2)),X1))
      | ( X2 = zero_zero_nat )
      | ( sK45(X0,hAPP_n1699378549t_bool(ord_less_nat,X1),X2) = X1 ) ),
    inference(superposition,[status(thm)],[c_1259,c_1706]) ).

tcf(c_112542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X3)
      | ( X3 = zero_zero_nat )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK45(X1,hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),X3))) ),
    inference(superposition,[status(thm)],[c_1262,c_1706]) ).

tcf(c_112543,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP4(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK45(X1,hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)),X2))
      | ( X0 = zero_zero_nat ) ),
    inference(superposition,[status(thm)],[c_1295,c_1706]) ).

tcf(c_121576,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(zero_zero_nat,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X1),X0)),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46504,c_1705]) ).

tcf(c_121641,plain,
    ! [X0: $i,X1: $i] :
      ( sP4(zero_zero_nat,hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(X0),X1)),zero_zero_nat)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(superposition,[status(thm)],[c_46506,c_1705]) ).

tcf(c_123609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( sP2(X2,X0,X3)
      | ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X0)),number_number_of_nat(X1)) = number_number_of_nat(X1) ) ),
    inference(superposition,[status(thm)],[c_1661,c_175]) ).

tcf(c_126603,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_126573,c_126572,c_126569,c_126565,c_126564,c_126563,c_126562,c_126559,c_126535,c_126534,c_126533,c_126532,c_126531,c_126530,c_126529,c_126528,c_126527,c_126507,c_126506,c_126505,c_126504,c_126469,c_126468,c_126467,c_126466,c_126465,c_126464,c_126462,c_126242,c_126234,c_126233,c_126232,c_126231,c_126230,c_126229,c_126228,c_126227,c_126226,c_126225,c_126224,c_126223,c_126222,c_126221,c_126220,c_126219,c_126218,c_126217,c_126216,c_126215,c_126214,c_126213,c_126212,c_126211,c_126210,c_126209,c_126208,c_126207,c_126205,c_126204,c_126201,c_126200,c_126198,c_126196,c_126195,c_126193,c_126192,c_126191,c_126190,c_126189,c_126188,c_126187,c_126186,c_126185,c_126183,c_126182,c_126181,c_126180,c_126179,c_126178,c_126177,c_126176,c_126175,c_126174,c_126172,c_126170,c_126184,c_126173,c_126155,c_126152,c_126151,c_126150,c_126141,c_126139,c_126138,c_126134,c_126131,c_126129,c_126105,c_126090,c_126089,c_126085,c_126081,c_126079,c_126078,c_126077,c_125919,c_125915,c_125864,c_125861,c_125860,c_125836,c_125833,c_125830,c_125824,c_125823,c_125822,c_125821,c_125820,c_125819,c_125818,c_125817,c_125816,c_125815,c_125814,c_125813,c_125812,c_125811,c_125810,c_125809,c_125808,c_125807,c_125806,c_125805,c_125804,c_125803,c_125802,c_125800,c_125799,c_125798,c_125797,c_125796,c_125795,c_125794,c_125793,c_125792,c_125791,c_125790,c_125789,c_125788,c_125787,c_125786,c_125785,c_125783,c_125782,c_125781,c_125780,c_125779,c_125778,c_125672,c_125668,c_125646,c_125645,c_125644,c_125643,c_125639,c_125638,c_125637,c_125636,c_125635,c_125634,c_125633,c_125632,c_125631,c_125630,c_125602,c_125601,c_125366,c_125342,c_125338,c_125314,c_125301,c_125300,c_125299,c_125298,c_125297,c_125296,c_125295,c_125294,c_125293,c_125292,c_125291,c_125290,c_125289,c_125288,c_125287,c_125286,c_125285,c_125284,c_125283,c_125282,c_125281,c_125280,c_125278,c_125277,c_125276,c_125275,c_125274,c_125273,c_125272,c_125271,c_125270,c_125269,c_125268,c_125267,c_125266,c_125265,c_125264,c_125263,c_125262,c_125261,c_125260,c_125179,c_125178,c_125177,c_125176,c_125172,c_125171,c_125170,c_125169,c_125168,c_125167,c_125166,c_125165,c_125164,c_125163,c_125034,c_125033,c_125032,c_125031,c_125027,c_125026,c_125025,c_125024,c_125023,c_125022,c_125021,c_125020,c_125019,c_125018,c_124568,c_124562,c_124561,c_124555,c_124554,c_124517,c_124516,c_124515,c_124514,c_124513,c_124512,c_124511,c_124510,c_124509,c_124508,c_124507,c_124506,c_124505,c_124504,c_124503,c_124502,c_124501,c_124500,c_124499,c_124498,c_124497,c_124496,c_124495,c_124494,c_124493,c_124492,c_124491,c_124490,c_124489,c_124488,c_124487,c_124486,c_124485,c_124484,c_124483,c_124481,c_124480,c_124479,c_124478,c_124477,c_124476,c_124475,c_124474,c_124473,c_124472,c_124471,c_124470,c_124469,c_124468,c_124467,c_124466,c_124465,c_124464,c_124463,c_124462,c_124461,c_124460,c_124459,c_124458,c_124457,c_124456,c_124455,c_124454,c_124453,c_124452,c_124451,c_124450,c_124449,c_124448,c_124447,c_124446,c_124445,c_124444,c_124443,c_124442,c_124441,c_124440,c_124439,c_124438,c_124437,c_124436,c_124435,c_124434,c_124433,c_124432,c_124431,c_124430,c_124429,c_124428,c_124427,c_124426,c_124425,c_124424,c_124423,c_124422,c_124421,c_124420,c_124419,c_124418,c_124417,c_124416,c_124415,c_124414,c_124413,c_124412,c_124411,c_124410,c_124409,c_124408,c_124347,c_124343,c_124336,c_124335,c_124334,c_124333,c_124329,c_124328,c_124327,c_124326,c_124325,c_124324,c_124323,c_124322,c_124321,c_124320,c_124229,c_124227,c_124148,c_124147,c_124146,c_124145,c_124141,c_124140,c_124139,c_124138,c_124137,c_124136,c_124135,c_124134,c_124133,c_124132,c_124114,c_124113,c_124112,c_124111,c_124110,c_124109,c_124108,c_124107,c_124106,c_124105,c_124103,c_124102,c_124082,c_124081,c_124080,c_124079,c_124078,c_124077,c_124076,c_124075,c_124074,c_123997,c_123993,c_123989,c_123929,c_123925,c_123921,c_123917,c_123913,c_123909,c_123905,c_123901,c_123897,c_123893,c_123889,c_123885,c_123881,c_123877,c_123873,c_123869,c_123865,c_123861,c_123857,c_123853,c_123849,c_123845,c_123841,c_123837,c_123833,c_123831,c_123830,c_123829,c_123828,c_123827,c_123826,c_123825,c_123824,c_123823,c_123822,c_123821,c_123820,c_123819,c_123818,c_123817,c_123816,c_123815,c_123814,c_123813,c_123812,c_123811,c_123810,c_123809,c_123808,c_123807,c_123806,c_123805,c_123804,c_123803,c_123802,c_123801,c_123800,c_123799,c_123798,c_123797,c_123796,c_123795,c_123794,c_123793,c_123792,c_123791,c_123790,c_123660,c_123659,c_123658,c_123654,c_123653,c_123652,c_123651,c_123650,c_123646,c_123645,c_123644,c_123657,c_123634,c_123632,c_123629,c_123628,c_123625,c_123614,c_123612,c_123611,c_123609,c_123546,c_123539,c_123533,c_123532,c_123529,c_123528,c_123527,c_123526,c_123525,c_123524,c_123523,c_123522,c_123521,c_123518,c_123516,c_123515,c_123511,c_123510,c_123509,c_123508,c_123507,c_123506,c_123505,c_123504,c_123503,c_123502,c_123501,c_123500,c_123499,c_123498,c_123497,c_123496,c_123495,c_123494,c_123493,c_123492,c_123491,c_123490,c_123489,c_123488,c_123487,c_123486,c_123485,c_123482,c_123480,c_123479,c_123140,c_123136,c_123135,c_123134,c_123133,c_123132,c_123126,c_123125,c_123122,c_123121,c_123120,c_123119,c_123118,c_123117,c_123116,c_123115,c_123114,c_123111,c_123109,c_123108,c_123104,c_123103,c_123102,c_123101,c_123100,c_123099,c_123098,c_123097,c_123096,c_123095,c_123094,c_123093,c_123092,c_123091,c_123090,c_123089,c_123088,c_123087,c_123086,c_123085,c_123084,c_123083,c_123082,c_123081,c_123079,c_123078,c_123075,c_123073,c_123072,c_123080,c_123069,c_123068,c_123067,c_123066,c_123065,c_123064,c_123063,c_123062,c_123061,c_123060,c_123059,c_123058,c_123057,c_123056,c_123055,c_123054,c_123053,c_123052,c_123051,c_123050,c_123049,c_123048,c_123047,c_123046,c_123045,c_123044,c_123043,c_123042,c_123041,c_123040,c_123039,c_123038,c_123037,c_123036,c_123035,c_123034,c_123033,c_123032,c_123031,c_123030,c_123029,c_123028,c_123027,c_123026,c_123025,c_123024,c_123023,c_123022,c_123021,c_123020,c_123019,c_123018,c_123017,c_123016,c_123015,c_123014,c_123013,c_123012,c_123011,c_123010,c_123009,c_123008,c_123007,c_123006,c_123005,c_123004,c_123003,c_123002,c_123001,c_123000,c_122999,c_122998,c_122997,c_122996,c_122995,c_122994,c_122993,c_122992,c_122991,c_122990,c_122989,c_122988,c_122987,c_122986,c_122985,c_122984,c_122982,c_122981,c_122979,c_122978,c_122977,c_122976,c_122899,c_122892,c_122886,c_122885,c_122882,c_122881,c_122880,c_122879,c_122878,c_122877,c_122876,c_122875,c_122874,c_122871,c_122869,c_122868,c_122864,c_122863,c_122862,c_122861,c_122860,c_122859,c_122858,c_122857,c_122856,c_122855,c_122854,c_122853,c_122852,c_122851,c_122850,c_122849,c_122848,c_122847,c_122846,c_122845,c_122844,c_122843,c_122842,c_122841,c_122840,c_122839,c_122836,c_122834,c_122833,c_122544,c_122540,c_122539,c_122538,c_122537,c_122536,c_122530,c_122529,c_122526,c_122525,c_122524,c_122523,c_122522,c_122521,c_122520,c_122519,c_122518,c_122515,c_122513,c_122512,c_122508,c_122507,c_122506,c_122505,c_122504,c_122503,c_122502,c_122501,c_122500,c_122499,c_122498,c_122497,c_122496,c_122495,c_122494,c_122493,c_122492,c_122491,c_122490,c_122489,c_122488,c_122487,c_122486,c_122484,c_122483,c_122480,c_122478,c_122477,c_122485,c_122474,c_122473,c_122472,c_122471,c_122470,c_122469,c_122468,c_122467,c_122466,c_122465,c_122464,c_122463,c_122462,c_122461,c_122460,c_122459,c_122458,c_122457,c_122456,c_122455,c_122454,c_122453,c_122452,c_122451,c_122450,c_122449,c_122448,c_122447,c_122446,c_122445,c_122444,c_122443,c_122442,c_122441,c_122440,c_122439,c_122438,c_122437,c_122436,c_122435,c_122434,c_122433,c_122432,c_122431,c_122430,c_122429,c_122428,c_122427,c_122426,c_122425,c_122424,c_122423,c_122422,c_122421,c_122420,c_122419,c_122418,c_122417,c_122416,c_122415,c_122414,c_122413,c_122412,c_122411,c_122410,c_122409,c_122408,c_122407,c_122406,c_122405,c_122404,c_122403,c_122402,c_122401,c_122400,c_122399,c_122398,c_122397,c_122396,c_122395,c_122394,c_122393,c_122392,c_122391,c_122389,c_122388,c_122386,c_122385,c_122384,c_122383,c_122340,c_122333,c_122327,c_122326,c_122323,c_122322,c_122321,c_122320,c_122319,c_122318,c_122317,c_122316,c_122315,c_122312,c_122310,c_122309,c_122305,c_122304,c_122303,c_122302,c_122301,c_122300,c_122299,c_122298,c_122297,c_122296,c_122295,c_122294,c_122293,c_122292,c_122291,c_122290,c_122289,c_122288,c_122287,c_122286,c_122285,c_122284,c_122283,c_122282,c_122281,c_122278,c_122276,c_122275,c_122082,c_122078,c_122077,c_122076,c_122075,c_122074,c_122068,c_122067,c_122064,c_122063,c_122062,c_122061,c_122060,c_122059,c_122058,c_122057,c_122056,c_122053,c_122051,c_122050,c_122046,c_122045,c_122044,c_122043,c_122042,c_122041,c_122040,c_122039,c_122038,c_122037,c_122036,c_122035,c_122034,c_122033,c_122032,c_122031,c_122030,c_122029,c_122028,c_122027,c_122026,c_122025,c_122023,c_122022,c_122019,c_122017,c_122016,c_122024,c_122013,c_122012,c_122011,c_122010,c_122009,c_122008,c_122007,c_122006,c_122005,c_122004,c_122003,c_122002,c_122001,c_122000,c_121999,c_121998,c_121997,c_121996,c_121995,c_121994,c_121993,c_121992,c_121991,c_121990,c_121989,c_121988,c_121987,c_121986,c_121985,c_121984,c_121983,c_121982,c_121981,c_121980,c_121979,c_121978,c_121977,c_121976,c_121975,c_121974,c_121973,c_121972,c_121971,c_121970,c_121969,c_121968,c_121967,c_121966,c_121965,c_121964,c_121963,c_121962,c_121961,c_121960,c_121959,c_121958,c_121957,c_121956,c_121955,c_121954,c_121953,c_121952,c_121951,c_121950,c_121949,c_121948,c_121947,c_121946,c_121945,c_121944,c_121943,c_121942,c_121941,c_121940,c_121939,c_121938,c_121937,c_121936,c_121935,c_121934,c_121933,c_121932,c_121930,c_121929,c_121927,c_121926,c_121925,c_121924,c_121786,c_121779,c_121773,c_121772,c_121769,c_121768,c_121767,c_121766,c_121765,c_121764,c_121763,c_121762,c_121761,c_121758,c_121756,c_121755,c_121751,c_121750,c_121749,c_121748,c_121747,c_121746,c_121745,c_121744,c_121743,c_121742,c_121741,c_121740,c_121739,c_121738,c_121737,c_121736,c_121735,c_121734,c_121733,c_121732,c_121731,c_121730,c_121729,c_121728,c_121725,c_121723,c_121722,c_121712,c_121711,c_121710,c_121708,c_12170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).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : NUM926+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.45  % Computer : n018.cluster.edu
% 0.11/5.45  % Model    : x86_64 x86_64
% 0.11/5.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.45  % Memory   : 8046.5625MB
% 0.11/5.45  % OS       : Linux 6.8.0-71-generic
% 0.11/5.45  % CPULimit : 300
% 0.11/5.45  % WCLimit  : 300
% 0.11/5.45  % DateTime : Thu Sep 24 05:47:09 UTC 2026
% 0.11/5.45  % CPUTime  : 
% 0.11/5.45  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.48  Running first-order theorem proving
% 0.11/5.48  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.50  
% 0.11/5.50  % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.50  
% 0.15/5.50  % Detected problem language: tptp
% 0.15/5.51  % Proving...
% 123.21/22.59  % SZS status Started for theBenchmark.p
% 123.21/22.59  ERROR - "ProverProcess:heur/469571:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  ERROR - cmd was:  ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 6 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3.0 --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 32 --inst_dismatching false --inst_eager_unprocessed_to_passive false --inst_eq_res_simp false --inst_learning_factor 10 --inst_learning_loop_flag true --inst_learning_start 256 --inst_lit_activity_flag true --inst_lit_sel "[+sign;-ground;-non_prol_conj_symb;-num_var]" --inst_lit_sel_side num_lit --inst_orphan_elimination true --inst_passive_queue_type list --inst_passive_queues "[[-ground;-epr]]" --inst_passive_queues_freq "[2]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 0.6939020527068606 --inst_solver_per_active 8 --inst_sos_flag false --inst_start_prop_sim_after_learn 9 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 2048 --prop_solver_per_cl 128 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[DemodLightNormLoopTriv;ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 640 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify   -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/9uz_3sni 2>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/9uz_3sni_error
% 123.21/22.59  ERROR - "ProverProcess:heur/397442:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  ERROR - cmd was:  ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 64 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 4 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 2 --inst_lit_activity_flag false --inst_lit_sel "[-split]" --inst_lit_sel_side num_lit --inst_orphan_elimination false --inst_passive_queue_type priority_queues --inst_passive_queues "[[+conj_symb]]" --inst_passive_queues_freq "[50]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.8199321230744955 --inst_solver_per_active 4 --inst_sos_flag false --inst_start_prop_sim_after_learn 7 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify   -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/ijci15ye 2>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/ijci15ye_error
% 123.21/22.59  ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 123.21/22.59  ERROR - cmd was:  ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify   -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/w_4du_7x 2>> /export/starexec/sandbox/tmp/iprover_out_z2rclzh4/w_4du_7x_error
% 123.21/22.59  % SZS status Theorem for theBenchmark.p
% 123.21/22.59  
% 123.21/22.59  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 123.21/22.59  
% 123.21/22.59  % ------  iProver source info
% 123.21/22.59  
% 123.21/22.59  % git: date: 2026-07-19 20:42:38 +0200
% 123.21/22.59  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 123.21/22.59  % git: non_committed_changes: false
% 123.21/22.59  
% 123.21/22.59  % ------ Parsing...
% 123.21/22.59  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 123.21/22.59  
% 123.21/22.59  % ------ Preprocessing... sup_sim: 332  sf_s  rm: 7 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 123.21/22.59  
% 123.21/22.59  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 123.21/22.59  
% 123.21/22.59  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 123.21/22.59  % ------ Proving...
% 123.21/22.59  % ------ Problem Properties 
% 123.21/22.59  
% 123.21/22.59  % 
% 123.21/22.59  % clauses                               1097
% 123.21/22.59  % conjectures                           0
% 123.21/22.59  % EPR                                   17
% 123.21/22.59  % Horn                                  907
% 123.21/22.59  % unary                                 298
% 123.21/22.59  % binary                                375
% 123.21/22.59  % lits                                  2570
% 123.21/22.59  % lits eq                               534
% 123.21/22.59  % fd_pure                               0
% 123.21/22.59  % fd_pseudo                             0
% 123.21/22.59  % fd_cond                               83
% 123.21/22.59  % fd_pseudo_cond                        47
% 123.21/22.59  % AC symbols                            0
% 123.21/22.59  
% 123.21/22.59  % ------ Schedule dynamic 5 is on 
% 123.21/22.59  
% 123.21/22.59  % ------ no conjectures: strip conj schedule 
% 123.21/22.59  
% 123.21/22.59  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 123.21/22.59  
% 123.21/22.59  
% 123.21/22.59  % ------ 
% 123.21/22.59  % Current options:
% 123.21/22.59  % ------ 
% 123.21/22.59  
% 123.21/22.59  
% 123.21/22.59  % 
% 123.21/22.59  
% 123.21/22.59  % ------ Proving...
% 123.21/22.59  % 
% 123.21/22.59  
% 123.21/22.59  % SZS status Theorem for theBenchmark.p
% 123.21/22.59  
% 123.21/22.59  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 124.27/22.84  
% 124.27/22.84  
%------------------------------------------------------------------------------